"Do you want domestic Parmesan or our special imported Parmesan that comes all the way from Argentina?" asked the pleasant woman behind the counter of the gourmet cheese shop.

Actually what I wanted was Parmesan for Parma, and I was learning my first lesson in Washington food shopping: Stay out of the gourmet cheese shops, gourmet supermarkets, gourmet delis and all the other places that stick the word "gourmet" somewhere on a sign in front - because they charge more for and know less about the food they sell than the ethnic stores do. And they frequently do not even carry the real ethnic food. There's nothing wrong with Argentina cheese - but you should eat it with Argentina food, shouldn't you?

It's a little hard to find real Italian stores in Washington - unlike many big cities, there never was a main Italian neighborhood here. But the stores are there, at least three. All carry real Parmesan, at least as cheap as the Argentina cheese. I found in the gourmet shop. All make their own sausage - hot or mild, regular or fennel-Flavored. Fennel flavored sausage - and never, never meatballs made of beef - is what the person who taught me how to cook Italian food insisted on in tomato sauce.

LITTERI'S, 517 Morse St. NE., in the Florida Avenue Market (LI 4-0183). From the outside the green metal doors and cinderblock facade of Litteri's look like the back end of a supermarket; and the inside looks the same way. In the small space beyond is concentrated the largest and cheapest selection of Italian specialties in the city. Parmesan cheese from Parma ($4.95 a pound, 55 cents less than the gourmet shop's Argentina). Dececco pasta (59 cents a pound), Licca olive oil ($3.25 a quart, $11.75 a gallon). Litteri's carries proscuitto, the Italian ham with the salty mild flavor and soft, almost buttery texture when sliced razor-thin. Even here, Italian prosciutto cost $6.25 a pound, but it is the real stuff, made in Italy, and made from nothing but pork, salt and pepper - no coloring, no chemicals, no nitrite carcinogens. There are also gallon cans of tomatoes at very low prices, Italian tuna, frozen pasta, bulk olives from Italy and Greece, and a small but very varied collection of jug wines. Among them is Segesta, the Sicilian wine that comes in the Italian equivalent of a jug - a bottle with a metal cap like a soda bottle and an old-fashioned china stopper for recapping. You might like to try Segesta because 1) opening wine with a bottle opener will amaze your friends, 2) this is the world's greatest spaghetti wine, and 3) the empty bottle can be filled with olive oil from a gallon can, making things easier in the kitchen if you keep it right beside the stove.

MANCUSO's FOODS, 2208 Rhode Island Ave. NE (LA 9-6225). Mancuso's keeps safe behind a locked door and lots of protective wire screening. Its cheese is cheap and ready-ground; its sausage the cheapest of any of the three stores; and the prices for pasta and tomatoes, while a few cents higher than Litteri's, are still much below supermarket level. There is a surprising variety of food in this very small store. Mrs. Mancuso seems to be the easiest person in any of the stores to talk to about recipes - an added value that the beginning Italina cook may find worth the trip.

MANGIALARDO'S, 1317 Pennsylvanis Ave. SE (LI 3-6213). Stay out of Mangialardo's around lunchtime when it fills up with GS-11s in conservative suits, burly guys remodeling Capitol Hill houses, passing policemen and shoppers looking for the big cheap sandwiches. Or come in at lunchtime and buy yourself a G-man Hero, which makes a very good lunch. Save your serious shopping for later in the day. Prices run about the level of Mancuso's. Mangialardo's Parmesan costs $5.69 a pound, but it is cut from a large wheel (Litteri's comes in precut wedges), which makes it better for eating if not for grating. The variety of Italian specialities is almost as great as Litteri's, and Mangialardo's also sells amoretti, those little Italian macaroons made of apricot kernels that may be the best cookies you ever tasted. Gourmet shops sometimes sell these cookies, too - in cardboard boxes, at something like $5.50 for 10 ounces. At Mangialardo's they come in lidded tins, kept out of the air so that they stay crispy and crunchable, at $5.79 a pound. And you also get a little booklet telling you how to enjoy amoretti - "Suggestion: Give amoretti to older persons to increase well-being. suggestion: Eat amoretti while watching TV. A treat missed." Plus directions for twisting the paper wrapper into a cylinder, lighting it and having it take off into the air! Making this a totally biodegradable delight.