To cook the lobsters: Follow the procedure as directed in the Maine Lobster Potpie, reserving the body for the Lobster Stock. Split the lobster tails in half lengthwise, keeping them in the shell, and set aside for the salad. Chop the claw and knuckle meat into large pieces and reserve for the soup. You should have about 1 cup.

Preheat the broiler or preheat and oil a grill.

Rub the lobster tails with the oil and season well with salt and pepper. Place them on a baking sheet, flesh side up, and broil for about 5 minutes, until the meat is slightly charred on the edges. Alternatively, place the lobster tails flesh side down on an outdoor grill and grill for 3 minutes. Turn the lobster tails over, using tongs, and cook the shell side for 2 minutes.

Immediately transfer the lobster tails to the refrigerator or freezer to stop the cooking process. Once the tails are cool, pull the meat from the shell. Cover and chill until ready to use for the salad.