DIRECTIONS:

1. Melt 1/2 stick butter over moderate heat in a large saucepan, and add carrots, celery, and onions. Cook until the vegetables are soft. 
2. Separate the lobster into tail pieces and claws. Add lobster sections to the vegetables, and sauté over moderately high heat until shells turn red. Remove lobster pieces from the pan, and remove the meat from the tails and claws. Reserve meat.
3. Chop all the shells into smaller pieces and return to the pan. Add 1/4 cup cognac and ignite. When flames subside, add wine, water, garlic, tarragon, and bay leaf. Stir to combine. Crush tomatoes and add to the pot along with the coarse salt and white pepper. Simmer over low heat for 45 mins. 
4. Pull out as many pieces of shell as possible and put the rest of the soup through  a sieve. Return milled broth to pan, and add reserved lobster meat and the rice. Simmer over low heat until reduced to 2 cups.
5. Take reserved shells and place in the bowl of a food processor. Pulse processor for about 30 seconds. Melt the remaining 1 stick butter in a medium saucepan and add chopped shells. Cook for 20 mins. Transfer to a fine sieve placed over a bowl.  Reserve butter and discard solids.
6. Remove reduced broth from heat. Purée in a blender and put through a fine sieve set over a  bowl. Return to pot, add lobster butter.
7. Add the remaining 1 tablespoon cognac to bisque, and heat for 5 to 7 mins. Add cream and milk and heat through. Garnish with tarragon.