1. Split the lobster in half. Twist off the claws and legs, break the claw apart at the joints, and crack the shells. Remove all meat from the lobster, chop the meat into small pieces, cover, and refrigerate. Chop the shell into rough pieces.

2. Heat the butter in a large saucepan over medium heat. Add the onion, carrot, celery, leek, fennel, garlic, tarragon, and bay leaf. Cook, stirring occasionally, for about 10 minutes, until tender.

3. Add the lobster shells. Stir in the fish stock, Cognac, wine, tomatoes, tomato paste, and rice. Bring to a boil, then simmer for 1 hour.

4. Let cool. In batches, pulse the stock mixture in a blender to chop the shell into small pieces.

5. Strain through a coarse sieve, pressing through as much liquid as possible. Strain again through a fine sieve to be sure that no shell remains in the soup.

6. Return the soup to a boil. Stir in the cream and lemon juice, and season with cayenne, salt, and pepper. Stir in the lobster and heat through. Ladle into bowls, garnish with créme fraîche and chives, and serve hot.

Variation:

Crab Bisque: Substitute 1 cooked Dungeness crab for the lobster. Pull off the top shell, remove and discard the gills and grit sac. Pull off the legs and crack the claws. Remove all of the available meat from the crab, chop, and refrigerate. Reserve the crab shells to use in step 3. Cook 2 tbsp peeled and chopped fresh ginger with the vegetables in step 2.