01 - Bring a large pot of salted water to a boil. Add the 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 and reserve. Crush the shells for stock.
02 - In a large pot, heat olive oil and 2 tablespoons of butter over medium heat. Add onion, leek, carrot, celery, and garlic. Sauté 6–8 minutes until softened.
03 - Add the lobster shells to the pot. Sauté 5 minutes, stirring often, to develop flavor.
04 - Stir in tomato paste, bay leaf, thyme, peppercorns, and paprika. Cook for 1 minute.
05 - Pour in brandy; carefully ignite with a long match to flambé. Once flame subsides, add white wine. Simmer 3 minutes.
06 - Add fish stock. Bring to a boil, then reduce heat and simmer uncovered for 25 minutes.
07 - Strain the mixture through a fine sieve, pressing 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 to taste with salt and white pepper.
10 - Ladle bisque into warm bowls. Top with reserved lobster meat and chives.