Ingredients

1. 3 quarts water
2. Four 1 1/2 -pound live lobsters, split lengthwise
3. 1/4 cup pure olive oil
4. 1 pound fennel bulbs--halved, cored and coarsely chopped
5. 2 medium celery ribs, coarsely chopped
6. 1 medium carrot, coarsely chopped
7. 1 medium onion, coarsely chopped
8. 1 medium leek, halved lengthwise and coarsely chopped
9. 1 unpeeled head of garlic, halved crosswise
10. 1/2 cup all-purpose flour
11. 2 tablespoons tomato paste
12. 2 cups dry white wine
13. 3 tablespoons Armagnac or Cognac, plus more for serving
14. 1 thyme sprig
15. 1 bay leaf
16. Large pinch of saffron threads
17. 1 cup heavy cream
18. Salt and freshly ground pepper
19. 2 tablespoons finely chopped parsley

Directions

1. In a large stockpot, bring the water to a boil. Twist the claws and tails from the lobster bodies and set aside the bodies. Add the claws and tails to the boiling water. Simmer the tails until just cooked, about 3 minutes, and the claws until they turn bright red all over, about 8 minutes; transfer the pieces to a large bowl as they are done and reserve the cooking liquid. Let the lobster cool slightly. Crack the claws; remove the meat from the tails and claws, then cover and refrigerate.
2. Twist the legs from the lobster bodies and cut the bodies into large pieces. Heat the olive oil in a large enameled cast-iron casserole. Add the fennel, celery, carrot, onion, leek and garlic and cook over moderately high heat, stirring frequently, until the vegetables are browned, about 8 minutes.
3. Add the lobster legs and body pieces to the casserole and cook over high heat, stirring, until the shells start to brown, about 8 minutes. Sprinkle the flour evenly over the shells and stir well. Add the tomato paste and cook, stirring, until it starts to brown, about 3 minutes. Stir in the wine and Armagnac and simmer for 3 minutes. Stir in the thyme, bay leaf, saffron and the reserved lobster cooking liquid until smooth.
4. Simmer the broth over low heat, skimming occasionally, until very flavorful, about 1 1/2 hours. Strain the broth through a coarse sieve, pressing on the solids to extract as much liquid as possible. Return the broth to the casserole.
5. Add the heavy cream to the casserole and simmer for 5 minutes. Season the bisque with salt and pepper. Cut the reserved lobster tail and claw meat into 1-inch pieces. Add the lobster meat to the simmering bisque and cook until just heated through, about 1 minute. Add a splash of Armagnac to 8 soup plates. Ladle the lobster bisque into the soup plates, garnish with the parsley and serve.

Make Ahead

The recipe can be prepared through Step 4 and refrigerated for up to 1 day. Rewarm the broth before proceeding with the bisque.