01 - Bring a large pot of salted water to a rolling boil. Add live lobsters and cook for 7–8 minutes until shells turn bright red. Immediately transfer lobsters to ice water to halt cooking. Remove meat from claws, tails, and knuckles; reserve all shells. Dice lobster meat into bite-sized pieces and refrigerate until needed.
02 - In a large pot over medium heat, melt butter with olive oil. Add onion, carrot, celery, and garlic. Sauté for 6–8 minutes, stirring occasionally, until vegetables are softened and fragrant.
03 - Stir tomato paste into the vegetable mixture and cook for 2 minutes to develop depth. Add reserved lobster shells and cook for an additional 2 minutes, stirring constantly to coat shells and release oils.
04 - Pour white wine into the pot, scraping the bottom with a wooden spoon to release any browned bits. Allow wine to simmer and reduce for 2 minutes.
05 - Add seafood stock, bay leaf, thyme, and cayenne pepper. Bring mixture to a boil, then reduce heat to maintain a gentle simmer. Cook uncovered for 30 minutes to allow flavors to meld and base to thicken slightly.
06 - Remove and discard lobster shells and bay leaf. Use an immersion blender to purée the soup until completely smooth. Alternatively, transfer to a countertop blender in batches, being cautious with hot liquid.
07 - Return puréed bisque to the pot. Stir in apple cider vinegar, heavy cream, and refrigerated lobster meat. Simmer gently over low heat for 5 minutes to warm through the lobster. Season generously with salt and pepper.
08 - Ladle hot bisque into warmed bowls. Garnish with finely chopped fresh chives or parsley. Serve immediately with crusty bread.