01 - Bring a large pot of salted water to a boil. Add live lobsters and cook for 6 to 8 minutes until shells turn bright red. Transfer lobsters to an ice bath. Remove meat from shells and set aside. Reserve shells for stock preparation.
02 - Melt butter in a large pot over medium heat. Add chopped onion, carrot, and celery. Sauté for 5 to 6 minutes until softened. Stir in minced garlic and cook for one additional minute.
03 - Add tomato paste to the sautéed vegetables and cook, stirring, for 2 minutes to deepen flavors.
04 - Add reserved lobster shells (if used), dry white wine, seafood stock, bay leaf, and thyme sprigs. Bring the mixture to a simmer and cook uncovered for 25 to 30 minutes to extract flavors.
05 - Remove and discard lobster shells, bay leaf, and thyme. Purée the soup base until smooth using an immersion blender or a regular blender with care.
06 - Return the puréed soup to low heat. Stir in heavy cream and brandy. Season with salt and pepper. Gently simmer for 5 minutes without boiling.
07 - Dice larger lobster pieces as needed. Add lobster meat to the bisque and warm through for 2 to 3 minutes.
08 - Ladle bisque into serving bowls and garnish with finely chopped fresh chives.