Combine 3 cups water, clam juice, and 1/2 cup wine in an 8-quart stockpot; bring to a boil. Add lobsters; cover and cook 10 minutes or until bright red. Remove lobsters from pan, reserving liquid in pan. Cool lobsters. Remove meat from tail and claws. Discard any roe or tomalley. Chop meat; chill until ready to use. Place lobster shells in pan. Add remaining 2 cups water, 1 cup carrot, 1 cup celery, 1 cup onion, 1/2 cup fennel, broth, tarragon, thyme, parsley, and bay leaves; bring to a boil. Reduce heat, and simmer, partially covered, 1 1/2 hours. Drain through a fine sieve over a bowl; discard solids.
Melt butter in pan over medium heat; add remaining 1/2 cup carrot, remaining 1/2 cup celery, remaining 1/2 cup onion, remaining 1/2 cup fennel, and garlic; sauté 5 minutes. Add remaining 1/4 cup wine; cook 3 minutes or until liquid almost evaporates. Sprinkle flour over carrot mixture; cook 1 minute, stirring constantly. Stir in reserved cooking liquid and potato; cook 20 minutes or until potato is tender. Add tomatoes; cook 10 minutes. Place one-third of mixture in blender; process until smooth. Pour pureed mixture into a large bowl. Repeat procedure twice with remaining mixture. Return pureed mixture to pan. Stir in lobster, milk, cream, and brandy; cook 5 minutes over medium-low heat or until thoroughly heated (do not boil). Garnish with chive sprigs, if desired.