01 - Steam or boil live lobsters for 8 to 10 minutes until bright red. Cool, remove meat from tails, claws, and knuckles. Reserve shells and chop meat into bite-size pieces; refrigerate.
02 - Heat butter and olive oil in a large pot over medium heat. Add lobster shells, onion, carrot, celery, and garlic. Sauté for 8 to 10 minutes until vegetables soften and shells release fragrance.
03 - Incorporate tomato paste and cook for 2 minutes. Add white wine and cognac, scraping browned bits from the pot. Simmer for 2 minutes to reduce slightly.
04 - Pour in seafood stock, add bay leaf, thyme, and paprika. Bring to a boil, then reduce heat and simmer uncovered for 25 minutes.
05 - Remove and discard lobster shells and bay leaf. Purée the soup until smooth using an immersion blender or working in batches in a blender.
06 - Return soup to the pot, stir in heavy cream, and bring just to a simmer. Add reserved lobster meat and heat gently for 2 to 3 minutes. Season with salt and pepper to taste.
07 - Ladle the bisque into bowls, garnish with chopped chives or parsley if desired, and serve hot.