01 - If using live lobsters, bring a large pot of salted water to a boil. Add lobsters and cook for 7–8 minutes until bright red. Remove, cool slightly, then extract meat from claws and tails; chop into bite-size pieces and reserve. Save shells for broth.
02 - In a large pot, melt butter over medium heat. Add onion, carrot, and celery; sauté 5–6 minutes until softened. Add garlic and cook 1 minute more.
03 - Stir in tomato paste and cook for 2 minutes. Add lobster shells (if using), seafood stock, bay leaf, peppercorns, and thyme. Simmer uncovered for 25–30 minutes to extract flavor.
04 - Strain the broth, discarding solids. Return the liquid to the pot over medium heat.
05 - Add white wine and brandy; simmer for 5 minutes to reduce slightly.
06 - Stir in paprika, cayenne, and heavy cream. Simmer gently for 10 minutes.
07 - For a silky texture, puree the bisque with an immersion blender (or carefully in batches in a blender), then strain through a fine mesh sieve for extra smoothness.
08 - Add reserved lobster meat to the pot, season with salt and pepper, and gently heat through for 2–3 minutes.
09 - Ladle bisque into bowls, garnish with chives, and serve immediately.