Lobster Bisque. A more helpful answer.
Here is one I've made and it is very good. Maybe pick up one more lobster or a couple tails to make it since you just have some shells to use. If you decide not to make bisque, just freeze the shells until you have some shrimp shells or more lobster shells and create a flavorful broth to keep until you need it.
Lobster Bisque
From Sam Sifton
INGREDIENTS
Kosher salt
2 live lobsters, weighing around 3 pounds total
2 tablespoons olive oil
1 carrot, chopped
2 ribs celery, chopped
1 medium onion, chopped
2 cloves garlic, crushed
2 sprigs fresh thyme
2 sprigs fresh tarragon
2 tablespoons tomato paste
1 cup medium sherry
2 cups fish stock or clam broth
½ cup long-grain white rice
1 cup heavy cream
Cayenne pepper, to taste
PREPARATION
Fill a large pot with 1/2 inch of water. Stir in 2 teaspoons kosher salt and bring the water to a boil. Add the lobsters, cover with a tight-fitting lid and return the water to a boil. Once boiling, lower the heat to a gentle boil and cook the lobsters until they are bright red, about 12 minutes. Remove the lobsters, reserving the liquid. When the lobsters have cooled slightly, place them in a bowl and remove the meat from the claws and tail, again reserving any liquid that comes out of the shells. Chop the meat and refrigerate. Roughly chop the shells into small pieces and reserve, along with all the lobster remains.
Swirl the olive oil in a large pot over medium heat, then add the vegetables and herbs. Sweat until the onions are translucent, about 5 minutes, then increase the heat to medium-high and add the lobster shells and remains. Sauté for 5 to 6 minutes, then add the tomato paste and cook for an additional 3 to 4 minutes.
Add the sherry, then ignite or cook until the alcohol has evaporated. Add fish stock and 1 cup of the lobster-cooking liquid. Bring to a simmer and cook, covered, for 1 hour.