01 - If using live lobsters, bring a large pot of salted water to boil. Add lobsters and cook for 7-8 minutes until bright red. Remove and cool. Extract meat from tails and claws, reserving shells for broth. Chop meat into bite-sized pieces and refrigerate.
02 - Heat olive oil in a large saucepan over medium heat. Add onion, carrot, celery, and garlic; sauté for 5-6 minutes until softened.
03 - Stir in lobster shells, tomato paste, and cook for 2 minutes until aromatic.
04 - Deglaze with white wine, scraping any browned bits. Add seafood stock, bay leaf, and thyme; simmer gently for 30 minutes, skimming foam as needed.
05 - Remove and discard shells and bay leaf. Blend soup base with an immersion blender until smooth, or use a regular blender in batches.
06 - Return soup to pot. Stir in heavy cream and butter; simmer gently for 5 minutes.
07 - Add sherry vinegar and season to taste with salt and pepper.
08 - Add reserved lobster meat and warm through for 2 minutes without boiling.
09 - Ladle into warm bowls. Drizzle with extra sherry vinegar and garnish with chives, tarragon, or crème fraîche if desired.