Do not throw away shrimp shells. They contain a concentrated flavor that is not found in the meat itself, and a short simmer transfers that flavor to the water. The resulting liquid makes a ready base for shrimp pasta, soup, and sauce. You can also collect shells and freeze them until you have enough. The process takes 20–30 minutes and requires no additional ingredients.
Much of the flavor and color associated with shrimp comes from the shells and heads, not the meat. That is why a sauce made with only the meat may not taste much like shrimp. Heating the shells releases these compounds into the water; at the same time, pigment from the shells dissolves and gives the liquid an orange color. This is a resource that often goes straight into the trash in many kitchens and can be recovered at no cost.
Roast the shells and any heads in a wide pan over medium heat with a spoonful of oil; cook for a few minutes, until their color deepens and they become fragrant. Do not skip this step, because roasting brings out the main flavor. Then add enough water to cover them and simmer gently for 20–30 minutes. Do not boil vigorously; a hard boil clouds the liquid and gives it a bitter taste. Strain through a fine-mesh strainer without pressing the shells. If they do not fit in the pan, roast them in 2 batches; piled-up shells steam instead of roasting.
Water and shells alone are enough, but you can add a few other ingredients if you like. Onion, garlic, celery stalks, and parsley stems broaden the base. Tomato or tomato paste adds color and depth. Add a bay leaf and peppercorns during the last 10 minutes. Add no salt at all, or wait until the end, because the liquid will later be reduced in a dish and its salt will become concentrated. Do not extend the cooking time; unlike meat stock, shrimp stock does not need a long simmer. A spoonful of tomato paste can also deepen the color and make the sauce seem fuller.
Each batch of shells may be too small for a pot. The solution is to collect them: rinse the cleaned shells, drain them thoroughly, place them in a covered container or bag in the freezer, and label it with the date. Once you have enough, put them straight into the pan without thawing and follow the same method. The shells keep in the freezer for months, but they should be kept in a tightly sealed container to prevent odor transfer.
Cool the prepared liquid before using or storing it. Cool it in a wide, shallow container and refrigerate it within 2 hours; it is fine to put it in the refrigerator while still hot. The stock keeps for 3 to 4 days in the refrigerator and for months in the freezer; freezing it in ice-cube trays makes portioning easier. The same method applies to crab and lobster shells. Mussel and oyster shells are not used for this purpose because they have no flavor to extract. Put the leftover shells in a sealed bag and discard them promptly rather than leaving them exposed in the kitchen.