01 - If using live lobsters, bring a large pot of salted water to a boil. Add lobsters and cook for 7 to 8 minutes until bright red. Remove and allow to cool. Extract meat from tails and claws; reserve shells for broth. Chop meat into bite-sized pieces and refrigerate.
02 - In a large saucepan, heat olive oil over medium heat. Add onion, carrot, celery, and garlic; sauté for 5 to 6 minutes until softened and fragrant.
03 - Stir in lobster shells if using and tomato paste; cook for 2 minutes until aromatic and deepened in color.
04 - Deglaze the pan with dry white wine, scraping any browned bits from the bottom. Add seafood stock, bay leaf, and thyme. Simmer gently for 30 minutes, skimming any foam that rises to the surface.
05 - Remove and discard lobster shells and bay leaf. Blend soup base with an immersion blender until smooth, or transfer in batches to a regular blender for a refined consistency.
06 - Return soup to the pot. Stir in heavy cream and butter; simmer gently for 5 minutes without allowing it to boil.
07 - Add sherry vinegar and season to taste with salt and freshly ground black pepper, adjusting acidity and seasoning to preference.
08 - Add reserved lobster meat and warm through for 2 minutes, being careful not to boil the delicate shellfish.
09 - Ladle into warm bowls. Drizzle with additional sherry vinegar and garnish with chives, tarragon, or crème fraîche if desired.