IF THE WORKING (or just plain tired) parents of America ever organize, one of the first things they should do is give an award to the grilled cheese sandwich. With cheese prices rising constantly, cheese sandwiches are no longer the dirt-cheap item they once seemed to be; but they're still low-budget, and valued more dearly now in light of the current peanut butter crisis. Besides, it is hard to believe something so easy to make is (a) nutritious and (b) consummately edible.

Where I grew up, the only place you saw cheese was in a Tom and Jerry cartoon. Grilled cheese to us meant Wonder Bread, Velveeta and Oleomargarine (a sandwich not unlike the ones now served at dimestore lunch counters). Over the years, the grilled cheese sandwich, like the rest of us, has grown more sophisticated -- and the increased variety of cheeses and breads available has made it possible for us to borrow sandwich ideas from all over the world. The recipes below are much too good to restrict to children; they're equally good for casual lunches, Sunday brunches, family dinners and midnight, family dinners and mid-night suppers a deux (melted cheese is sexy even when it's not Brie). THE BASIC GRILLED CHEESE SANDWICH 1 or 2 slices, or an equivalent amount grated, meltable cheese, such as american, cheddar, swiss (emmentahal), gruyere, muenster, monterey jack, or mozzarella 2 slices bread, crust removed butter or margarine (optional)

Sandwich the cheese between the bread slices, and butter the outside of the bread before grilling it; this gives the bread a nice sauteed quality. (You can omit the butter, but it won't taste as good.) You want to melt the cheese thoroughly without scorching the bread, so cook the sandwich slowly -- possibly 3 or 4 minutes on each side -- at medium-low.

A waffle iron that reverses to become a 2-sided grill is good for grilling, but you can do quite well with a stovetop grill or skillet. If the bread and cheese slices are thick or the range unpredictable, grill the sandwiches in a skillet, putting a lid on for a while so the cheese will melt. The softer cheeses, like mozzarella and muenster, melt more easily than cheddar or the harder swisses. If the cheese if old and dry, it will melt more easily if you grate it first.

For variety, add tomato slices, alone, or with strips of nearly crisp bacon, mustard, mayonaise or even jam (though I couldn't bring myself to test the latter); hot pepper jelly (with or without a slice of ham); chutney (a friend raves about hot tomato chutney and mozzarella); sauteed onion slices and dijon mustard (like onion soup, in reverse); a thin slice of corned beef and onion (on rye bread, with swiss); sauerkraut and corned beef (on rye, with swiss), white tuna and tomato (often called a "tuna melt"); cooked green peppers, chopped pineapple or sliced apples, if you like that kind of taste. EARTH LILY 2 to 3 scallions, cut in 4-inch pieces 2 slices bacon 2 slices black bread 2 slices cheddar cheese

Wrap 3 green onion pieces with 2 slices bacon; arrange on rack in baking pans and bake in oven at 400 degrees for 15 minutes or until bacon is done.

To prepare each sandwich: On one slice of bread place 1 slice of cheese, 2 onion bundles and a second slice of cheese. Close the sandwich with a second slice of bread, and grill on both sides until cheese melts. You can do this in the oven. OPEN-FACE SANDWICHES

You can use any kind of bread for grilled cheese sandwiches, including muffins, croissants, tortillas and pita bread (see the recipes below), but they're such a good vehicle for sneaking whole-wheat into kids (who invariably prefer white) that this easy recipe has become a staple in our house. Preceded by vegetable soup, this is a wholesome meal. For each sandwich use: p 1 slice whole-wheat bread (crusts trimmed) Butter or margarine (optional, but tasty) Tomato slices, optional 1 thin slice cheddar or swiss (or 2 to 4 tablespoons grated)

Cover a broiling pan with aluminum foil (to avoid having to wash it later), arrange the slices of bread on it, butter them, arrange optional tomato slices in a flat layer on the bread, then top with cheese. Broil until cheese melts and -- if you like it that way (we don't ) -- is slightly browned. This doesn't take long, so keep an eye on things. If you habitually scorch things under the broiler, you may have better results "baking" the sandwiches in a 400-degree oven. CALIFORNIA SANDWICH

Who would ever think of putting avocado in a grilled cheese sandwich? Not me -- but I'm sure grateful to the clever person who did. I first tasted this marvelous sandwich at Arnold's Turtle, a pretty little Greenwich Village restaurant; but our family has developed many variations since, whenever there's a sale on avocados. Here's how Arnold's Turtle makes it: 1 slice whole-wheat pita bread 1/4 cup or so grated white remetless cheddar (available in health food stores) 1/2 avocado Lemon juice 1 tomato, cut into coarse chunks Small handful alfalfa sprouts

Make a slice along the side of the pita bread, and into the pocket thus formed, stuff the cheese. Melt the cheese pocket in the oven, at about 400 degrees. (We prop it open with a toothpick because we feel this makes the cheese melt faster, but it's kind of a nuisance and probably just lets us see the progress of its melting.) While the cheese is melting, slice or mash the avocado, sprinkling a few drops of lemon juice on any unused portion to keep it from darkening. When the cheese has melted, put the sliced or mashed avocado in the pocket, then the tomato chunks and sprouts -- as many or as few as you like. It's perfectly delicious without the tomatoes and sprouts but the red is pretty and the sprouts make you feel so virtuous.

A simple variation: Melt monterey jack cheese on a piece of pita bread, slice avocado on top, and salt it a little to bring out the flavor of the avocado. Or if you don't have an avocado, try this simple rendition: Spread a little oil on the flat bread, rub garlic on it, arrange thin slices or a layer of grated sharp cheese on the bread, and top this with oregano or another herb -- perhaps fresh thyme from your garden. QUESADILLAS

The nice thing about these Mexican "sandwiches" is that children can make them, if they're the least bit handy. My daughter periodically goes on quesadilla binges, eating two or three of them a day. They're easy, they're delicious, and they lend themselves to variation.For each sandwich, you'll need: 2 thing slices of monterey jack cheese 1 peeled green chili pepper (optional, especially for children) 1 tortilla, either corn or wheat (see note below)

Wash the chilies, remove the seeds, and drain off excess water. (Some people eat them the way they are.)

Turn the heat up under an iron or non-stick skillet until it's very warm. Don't put oil or any form of grease in the skillet unless you want a crunchy tortilla; if you like them soft, as we do, you don't need it. Put the tortilla in flat, and heat it until it is warm and soft. Put a strip of cheese and a peeled green chili on half of the tortilla, fold the tortilla over to a half-moon, turn the quesadila over once, continue heating it until the cheese has melted, remove from pan and eat immediately.

There are countless variations. You can skip the chili, melt the cheese, then splash a little hot sauce inside the tortilla. Or add a little chopped tomato, or chili sauce, or green tomato sauce, or avocado . . . sauce!) They're also good perfectly plain, just tortilla and cheese. And if you really love them, you can move into the big time with the more elaborate methods in Diana Kennedy's "The Cuisines of Mexico." MOZZARELLA IN CARROZZA (Mozzarella in a Carriage) 1 slice of mozzarella or Bel Paese 2 half slices of firm white bread (about-2-by-3-inches, to fit the cheese) Egg and milk batter (1 tablespoon of milk per egg) Enough butter or margarine and oil (or just oil) to cover the bottom of skillet, about 1/8-inch deep Anchovy fillets and butter, optional

First, get the sandwiches ready (a slice of cheese between two slices of bread), keeping them on the small side. Beat eggs and milk together in a bowl large enough to dip the sanwiches in. Heat the butter or margarine and oil in a skillet large enough to hold 3 or 4. When the oil is quite hot but not smoking, dip the sandwiches in the batter -- first the edges, then the sides -- and fry them quickly until golden brown on both sides, turning them once. Traditionally these are served with anchovy sauce (half a dozen anchovies dissolved in as many tablespoons of melted butter), but you may have trouble getting mere families to accept this unusual tast -- and I, anchovy lover, seldom miss it.

Some people use clarified butter to saute these sandwiches and the croque-monsieur (next recipe). You may find it easier to use half peanut or other vegetable oil and half butter or margarine. (Do not however, use olive oil, which has too sttrong a taste.) Fried in oil the sandwiches have a more Italian character. Fried in butter (which my children like better, alas) they taste more like super-deluxe French toast.

If you are feeling very fancy, Craig Claiborne's "New York Times International Cook Book" gives an elaborate recipe for shaping the bread as railway carriages in which the mozzarella rides. CORQUE-MONSIEUR

Variations on this French theme abound, but basically it's just a ham and cheese sandwich grilled slowly in butter, so that the chese melts and the bread has a crusty exterior. For each sandwich, you need: 2 slices white bread, crusts trimmed off Margarine or clarified butter 2 thin slices swiss, gruyere, or mozzarella to fit bread 1 thin slice baked ham, to fit bread

On a buttered slice of bread, buttered side up, put a thin slice of cheese, a thin slice of ham, another slice of cheese, and a buttered slice of bread. Saute this sandwich-within-a-sandwich in 2 tablespoons of margarine or clarified butter, or butter and oil, adding more if your need it. Sometimes I omit one piece of cheese and start by putting the ham in the skillet, topping it with the cheese, then one piece of buttered bread. When the cheese starts to melt, I turn the partial sandwich over and, as the downside piece of bread browns, add the second piece of bread. After a couple of minutes, I turn the whole sandwich over and brown the second piece of bread. This sounds complicated, but isn't, and I find doing it this way not only heats up the ham but also gets the cheese to melt faster.

Many cooks achieve a puffier looking exterior -- quite nice for a brunch -- by dipping the egg-and-ham sandwich in an egg-and-milk batter (1 tablespoon of milk per egg) and cooking it more or less the way you cook french toast. Doris McFerran Townsend, in a practical family cookbook called "Cheese Cookery," suggests topping the french-toasted cheese sandwich with a dollop of currant jelly. For a variation called croque-madame, she suggests substituting slices of cooking turkey breast for the ham, gruyere for swiss, and respberry jelly (surely optional) for currant. ("Cheese Cookery" is available for $5.95 -- plus .75 -- from HP Books, Box 5367, Tucson, Ariz. 85703.) CROISSANTS DES MOINES

One degree fancier and you could hardly classify these as grilled cheese sandwiches, but that's basically what they are -- very elegant for Sunday brunch and fairly easy for a late supper, too. Serve a litle something green on the side, and if you don't feel like cooking tonight, run down to Le Cellier des Moines in Georgetown and taste the original. For each sandwich, you need: Bechamel/Mornay sauces (for 6 croissants): 2 tablespoons butter or margarine 2 tablespoons flour 1 1/2 cups milk (extra cream optional) 1 small onion 1/2 cup grated swiss, gruyere or white cheddar Salt and pepper to taste Sandwiches: 6 croissants 12 thin slices mozzarella 6 thin slices baked ham

To make the sauce, in a heavy saucepan, melt the butter, stir in the flour with a wire whisk and, stirring constantly over low heat, cook the roux about 3 minutes to rid it of its floury taste, taking care not to let it brown. Add the milk (a little at a time, if cold; all at once, if heated first) and blend until smooth. Add the onion, peeled but not chopped, and cook the sauce on low heat until medium-thick. Discard the onion, pour half of the white sauce in a separate saucepan (keeping it warm on the side), and add about 1/2 cup of grated cheese to 1 panful of the bechamel, thus converting it into a simplified mornay sauce. Salt and pepper the sauces to taste, and add a little cream if the consistency isn't right.

To make the sandwiches, cut a fresh croissant in half and place it on a baking sheet. Put a small ladleful of mornay sauce over the croissant, then a thin slice of mozzarella, then a slice of ham, then another slice of cheese, then the other half of the croissant. Put this under the broiler until the cheese browns. (When we tested the recipe, we baked the sandwiches for about 8 minutes at 350 degrees and then ran them under the broiler.) Arrange the sandwiches on the serving plates, spoon a little bechamel sauce over them, and voila! Croissants des Moines (slightly adapted). SUMMERY MUFFINS

English muffins make an excellent vehicle for grilled cheese sandwiches, either plain or in variations. One possibility is a mini-pizza (muffin, thinly sliced tomato or tomato puree, mozzarella, optional grated parmesean, and oregano, grilled open-face. At the peak of tomato season, we are expecially fond of the following cream-cheese-and-chives creation, especially for brunch or breakfast. Technically it isn't grilled cheese, but the warmth of the toasted muffin softens the cream cheese, which then meshes gloriously with the tomato and chives -- truly delicious. Ideally, here is how you'll make it:

Take cream cheese from the refrigerator to soften. While someone else makes morning coffee or tea, go into the garden and pick a plump red tomato, and snip a handful of chives. (It's better to snip a few blades to within half an inch of the roots than to shave an inch off the whole clump, I am told.) Carry these into the kitchen, chop the chives, split a muffin and toast it, spread each side with a thin-to-medium layer of cream cheese, top one side with thin tomato slices, half a teaspoon or so of chopped chives, salt, and the other halkf of the muffin. Since this all tends to fall out, I generally wrap the bottom half of the sandwich with a paper towel or napkin, then dig in. In a pinch, you can make do with store-bought, vine-ripened tomatoes. LAUREL'S KITCHEN LOW-CAL CHEESE SPREAD

The authors of "Laruel's Kitchen" suggest combining grated natural cheese with an equal amount of low-fat cottage cheese to reduce the cost and calorie count of a cheese sandwich. They add 1 tablespoon of mayonnaise to each cup of this mixture, and vary the taste with ingredients such as finely chopped celery, minced parsley, diced hard-cooked egg, chopped chives or tomatoes, garlic, paprika or mustard powder. To 1 cup of the cheese mixture they particularly like to add 1/4 cup chopped green pepper, 1/2 teaspoon dill weed, and salt and pepper to taste. You can mix the ingredients together and chill them, serving them later on open-faced sandwiches -- either cold or toasted under the broiler.