In a large pot, melt the butter over medium heat. Add the lobster shells, onion, carrot, celery, and garlic. Sauté for about 5 minutes until the vegetables are softened. Stir in the tomato paste and cook for another 2 minutes.

Add the Wine and Stock

Pour in the white wine and bring to a simmer. Let it reduce by half, which should take about 5 minutes. Add the fish stock or seafood broth, bay leaf, salt, and black pepper. Bring to a boil, then reduce heat and let simmer for 30 minutes.

Blend the Soup

Remove the pot from heat and let cool slightly. Remove the lobster shells and bay leaf. Using an immersion blender, blend the soup until smooth. You can also transfer it to a blender in batches if needed.

Add Cream and Lobster

Return the blended soup to the pot. Stir in the heavy cream and chopped lobster meat. Heat gently over low heat until warmed through, about 5 minutes. Adjust seasoning to taste.

Serve

Ladle the lobster bisque into bowls and serve with crackers on the side.