Bring large pot of water to boil. Add lobsters head first and boil until cooked through, about 8 minutes.
Transfer lobsters to large bowl. Reserve 2 cups cooking liquid. Cool lobsters.
Working over large bowl to catch juices, cut off lobster tails and claws. Crack tail and claw shells and remove lobster meat.
Chop lobster meat; cover and chill. Coarsely chop lobster shells and bodies; transfer to medium bowl. Reserve juices from lobster in large bowl.
Heat olive oil in heavy large pot over high heat then add lobster shells and bodies and sauté until shells begin to brown, about 8 minutes.
Add onion and next 8 ingredients. Stir in brandy and Sherry. Boil until almost all liquid has evaporated, about 4 minutes.
Add fish stock, reserved 2 cups lobster cooking liquid and lobster juices. Simmer 1 hour.
Strain soup through sieve set over large saucepan, pressing firmly on solids. Whisk tomato paste into soup. Simmer until soup is reduced to 3 cups, about 15 minutes.
Add cream to soup and simmer 5 minutes.
Dissolve cornstarch in 1 tablespoon water. Add to soup and boil until slightly thickened, about 2 minutes. Combine lobster meat into soup and stir to heat through.
Ladle soup into 6 bowls and serve.
