French onion soup requires good stock, onions and cheese. (Tracy A. Woodward/THE WASHINGTON POST)

Few things are more promising than a piping-hot bowl of French onion soup placed before you on a brisk day, its fragrant liquid beneath a toasted raft topped with golden cheese that will soon be stringing from your mouth. How frustrating, then, to discover something skimpy, with bready mush and pale onions, devoid of flavor.

Having been subjected to three such disappointing examples at local restaurants in the fall, I decided to work through what it takes to make a soul-satisfying version. Not reinventing the wheel; just returning it to the right course.

Onions became the focal point of my tinkering with other cold-weather classics, including croque monsieur, baked stuffed onions and a savory tart.

The soup has three make-or-break components: broth, onions, cheese. An excellent rendition is layered with flavor and nuance. It starts with an excellent stock; without it, your soup will be average, at best. That means the store-bought stuff in cartons is out.

But stock on its own doesn’t guarantee success. To be honest, my first attempt was surprisingly weak even though I used homemade veal stock. Essentially, it’s best to make a stock from your stock; that is, bump it up by simmering it for 35 to 45 minutes with several skin-on onions (to deepen the stock’s color), celery with leaves (packed with flavor), thyme, black peppercorns and bay leaves. Don’t use carrots; caramelized onions will provide the final product with enough sweetness.

Having run out of veal stock, I used turkey stock and realized that any hearty meat stock (chicken, duck, beef) works in this soup as a fine foil for the onions. The best result, though, came to me by coincidence. I had smoked a couple of chickens for dinner the night before and had filled the drip pan underneath them with aromatics, the chicken’s neck and innards, and herbs. That yielded a rich, smoky stock that went into my soup because it was there; it really made the caramel quality of the onions pop and added a layer of flavor I hadn’t thought of before.

By the way, I’m not against using some bouillon cubes or onion powder or salt to add flavor, or even Kitchen Bouquet to deepen the color of a broth that looks wishy-washy.

Experimenting with yellow, white and Vidalia onions, I discovered that, yes, the Vidalias were sweetest; in fact, too much so to use on their own. I discerned little difference between the yellow and white onions. The soup versions with all yellow onions and half yellow/half Vidalia both had a fine balance of sweet to savory.

You will notice that when you cook onions, they become sweet and remain acrid at the same time, and their odor lingers for quite a while. That is because they contain a good amount of sulfur. When you cut onions, cells are crushed, releasing the sulfuric gas that induces tears that burn. I have no special trick for avoiding the problem, although I certainly have tried more than a few. Just power through the process — and use a food processor for slicing.

The goal in caramelizing onions is to get some color, and therefore flavor, on them quickly and cook them long enough to get rid of their water (10 cups of raw will reduce to barely two cups cooked) and deepen their flavor.

To that end, I place a large saute pan over medium-high heat. When it is very hot, I spread the onions in the pan and don’t touch them for several minutes so their moisture starts to evaporate. Then I add fat and still let them be for several minutes, until I notice that caramelization has begun. At that point, I season, stir, reduce the heat and cook for about 25 minutes, stirring and scraping up browned bits from the bottom every so often. Result: deeply browned strands of concentrated flavor and sweetness.

Into a pot they go with the stock for simmering and melding, fortified with bay leaves (for me, an integral ingredient in the caramelization process as well, because they imbue the onions with herbal and spice qualities) and finished with port wine (for its depth and caramel quality) and fresh chopped thyme. Adding those ingredients too soon diminishes their impact greatly.

Gruyere, a firm cow’s-milk cheese from Switzerland, is the standard for onion soup because of its distinctive nutty notes. But I found that a mixture of cheeses provided more complexity and interest. Plus, when Gruyere browns, it can leave a bitter aftertaste. After experimenting, I settled on semi-soft fontal, a melty and much less expensive Italian cheese, which added the creamy note I sought. I also tried, and rejected, combinations with raclette and fontina.

Along with the addition of caramelized onions, mixing cheeses made the difference in my version of croque monsieur. In addition to the fontal/Gruyere mix, I included a layer of Camembert. Remember, it’s all about layering the flavors — even for a grilled ham-and-cheese sandwich.

To build the sandwich, use soft butter on the outsides of bread slices and Dijon mustard on the insides for a nice acid note. I buy a country boule from a bakery. It has substance, and you can control the slice thickness. The airy crumb allows heat to get into the middle of the sandwich; you don’t want a hot sandwich with a cold center. Toast the sandwich over medium heat in a saute pan on both sides. If you rush it, it will toast before it cooks in the middle. For browning the cheese topping, use the upper third of the oven to broil (for a top-heating element).

Deli hams contain a lot of water. To ensure the sandwich would not be soggy, I microwaved the ham portions briefly between paper towels and blotted them before adding them.

While I was putting all this together, I eyed the sliced ham, Mornay sauce and caramelized onions sitting on the counter and had a light-bulb moment. Using scraps left over from making two pies that day, I rolled out a third crust and blind-baked it in a nine-inch tart pan.

It didn’t matter that the reworked pastry was a little tough. I wasn’t making a delicate dish. I covered the baked shell with the onions, topped them with ham and Mornay sauce and broiled what became a gooey, onion-soup-meets-croque-monsieur tart. A small slice makes a perfect winter first course; a larger one with a simple green salad is entree-worthy.

Could I make a meal of an onion by stuffing it? I could combine leftover caramelized onions with chard (more assertive than, say, spinach), hot Italian sausage for protein and heat, mushrooms for earthiness and volume, cream and Parmesan cheese for richness and panko as a binder. If you want the dish to be vegetarian, substitute a hearty grain such as farro for the sausage.

Onions must be scooped out and cooked through before stuffing, otherwise they will remain crunchy. As I scooped out large white ones to bake prior to stuffing, each yielded a cup of onion chunks. It didn’t make sense to use eight additional onions for caramelizing and waste the byproduct from what was to be stuffed, so I chopped the chunks into uniform pieces and caramelized them instead.

In an attempt to combine two steps, I roasted the hollowed-out onions on a layer of the chopped onions drizzled with oil, hoping that the latter would caramelize during the 40-minute cooking time. They cooked unevenly — some burned — and went into the trash.

For a second go, I placed the hollowed-out onions on a bed of the chopped onions and oven-steamed them in a foil-covered pan that really added nothing to the final result — except more work. Writing this, it occurs to me that reducing heavy cream into an easy sauce flavored with those onions, a fresh bay leaf, garlic, salt, pepper, thyme and rosemary (or the oregano that helped flavor the stuffing) would have added an elegant finishing touch to the dish.

Over the next few days, the caramelized onions from my various test batches got mixed with sour cream for a quick dip and heated with cream, chopped spinach and garlic for a side dish. I have no doubt that in the coming cold days and nights, with the aid of quarts of oniony broth in my freezer, I will be fulfilling the promise of a satisfying French onion soup.

Hagedorn’s column appears monthly in Food.