01 - Bring a large pot of salted water to boil. Add live lobsters and cook for 7-8 minutes until bright red. Remove and cool. Extract meat from tails and claws; reserve 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 and fragrant.
03 - Stir in reserved lobster shells and tomato paste; cook for 2 minutes until aromatic.
04 - Deglaze pan with dry white wine, scraping any browned bits. Add seafood stock, bay leaf, and thyme. Simmer gently for 30 minutes, skimming any foam that rises to surface.
05 - Remove and discard shells and bay leaf. Blend soup base with an immersion blender until completely smooth, or carefully transfer in batches to a standard blender.
06 - Return soup to pot. Stir in heavy cream and butter; simmer gently for 5 minutes without boiling.
07 - Add sherry vinegar and season to taste with salt and freshly ground black pepper.
08 - Add reserved lobster meat and warm through for 2 minutes, ensuring soup does not boil.
09 - Ladle into warm bowls. Drizzle with additional sherry vinegar and garnish with fresh chives, tarragon, or crème fraîche swirl if desired.