Fill a large pot with salted water and bring it to a rolling boil. Drop the live lobsters in and cook them until their shells turn bright red, about 5 to 6 minutes. Transfer the lobsters to an ice bath to cool, then remove all meat from tails, claws, and knuckles; chop it and set aside. Crush the lobster shells and keep them for the stock.

Warm olive oil and two tablespoons of butter in a big pot over medium heat. Add the onion, leek, carrot, celery, and garlic; cook, stirring frequently, until the vegetables are tender and fragrant, roughly 6 to 8 minutes.

Toss in the crushed lobster shells and sauté for about 5 minutes, stirring often to bring out a deep, toasty flavor.

Mix in the tomato paste, bay leaf, fresh thyme, peppercorns, and paprika; cook the mixture for 1 minute to release the spices’ aromas.

Pour the brandy into the pot and carefully ignite it with a long match to flambé. Once the flames fade, add the white wine and let it simmer gently for 3 minutes until it reduces a bit.

Add the fish or lobster stock and bring the mixture up to a boil. Lower the heat and let it simmer uncovered for 25 minutes to allow the flavors to meld beautifully.

Strain the broth through a fine sieve, pressing down on the solids to extract as much liquid as possible. Discard the solids and return the smooth bisque base back to the pot.

Stir in the heavy cream and most of the reserved lobster meat, keeping some aside for garnish. Warm the bisque gently for 5 minutes without boiling.

Take the pot off the heat, then add the remaining tablespoon of butter along with the sherry vinegar. Season carefully with salt and white pepper to taste. Serve the bisque in warmed bowls, topping each with reserved lobster meat and a sprinkle of fresh chives.