Boil lobsters and remove the meat. Dice the body meat and mince the tail and claw meat. Set it aside.
In a large pot, crush the shells. Add the tough end of the claws, the chicken stock, onion, celery, cloves, bay leaf and peppercorns. Simmer these ingredients for 30 minutes. Strain the stock and set it aside.
Melt the butter. Using a whisk, stir in the flour, then gradually add the milk and nutmeg. Season to taste with salt and pepper. When the sauce is smooth and has begun to boil, add the lobster and the stock. Simmer the bisque at medium heat, covered, for 5 minutes. In a small saucepan, warm the cream, but do not let it boil. Turn off the heat and stir in the cream.
Serve at once with minced parsley and paprika for color. Makes 6 cups.