Melt 1/4 cup butter in a large saucepan. Add the carrots, celery and onions and cook until soft, about 10 minutes. Add sections from 2 lobsters to pan and saute until shells turn red. Remove pieces from pan when cool enough and remove meat from tails and claws and reserve it.
Chop shells into smaller pieces and add to pan. Add 1/4 cup cognac and ignite. Then add the white wine, water, garlic, tarragon and bay leaf. Crush the drained tomatoes with hands and add to pot. Season with salt and pepper.
Simmer over low heat for 45 minutes, but do not allow liquid to boil. Remove as many pieces of shell as possible. Put soup through food mill and return milled broth to pan. Add the reserved lobster meat and 1/3 cup long grain white rice. Simmer over low heat another 45 minutes, or until reduced to 2 cups.
Pulse shells in a food processor until finely chopped. Melt 1/2 cup butter in a saute pan, add chopped shells and saute 5 minutes. Strain, reserving butter and discarding shells. Transfer reduced lobster-rice mixture to blender and puree. Strain the puree through a sieve over a mixing bowl and return broth to pot. Add the lobster butter and stir well. Add 1 tablespoon of cognac and heat for 5 to 7 minutes. Add the light cream and milk. Heat through, but do not boil.
Recipe courtesy of David Rosengarten