How to Make It
Bring 15 quarts of water and salt to a boil in a 19-quart stockpot; plunge lobsters headfirst, 1 at a time, into water. Return to a boil. Cover, reduce heat, and simmer 8 minutes for small lobsters (1 to 1 1/4 pounds) and 10 minutes for larger lobsters (1 1/2 to 2 1/2 pounds). Drain well; cool completely.
Remove meat from cooked lobster tails and claws; reserve meat for another use. Rinse out head portion of lobsters. Place lobster shells in a large heavy-duty zip-top plastic bag. Coarsely crush shells using a meat mallet or rolling pin.
Heat oil in a Dutch oven over medium-high heat. Add fennel and next 5 ingredients (fennel through onion); sauté 5 minutes or until vegetables are lightly browned. Add 3 quarts of water, crushed shells, wine, parsley, and thyme; bring to a boil. Reduce heat, and simmer 1 hour. Strain shell mixture through a sieve over a bowl, reserving stock. Discard solids.