01 - Bring a large pot of salted water to a boil. Add lobsters and cook for 5–6 minutes until bright red. Remove and transfer to an ice bath. Once cool, extract all meat from tails, claws, and knuckles. Chop meat and reserve. Crush shells for stock base.
02 - Heat olive oil and 2 tablespoons butter in a large pot over medium heat. Add onion, leek, carrot, celery, and garlic. Sauté for 6–8 minutes until softened and fragrant.
03 - Add crushed lobster shells to the pot. Sauté for 5 minutes, stirring frequently, to develop deep flavor and toast the shells.
04 - Stir in tomato paste, bay leaf, thyme sprigs, peppercorns, and paprika. Cook for 1 minute to bloom the spices and paste.
05 - Pour in brandy and carefully ignite with a long match to flambé. Once flame subsides, add white wine. Simmer for 3 minutes to reduce slightly.
06 - Add fish stock and bring to a boil. Reduce heat and simmer uncovered for 25 minutes to infuse flavors.
07 - Strain mixture through a fine sieve, pressing firmly to extract all liquid. Discard solids. Return bisque base to the pot.
08 - Stir in heavy cream and reserved lobster meat (save some for garnish). Simmer gently for 5 minutes.
09 - Remove from heat. Stir in remaining 1 tablespoon butter and sherry vinegar. Season with salt and white pepper. Ladle into warm bowls, top with reserved lobster meat and chives.