Start by heating the butter and olive oil in a large pot over medium heat. Once melted, add the onion, celery, and carrot. Cook slowly, stirring often, until the vegetables are very soft and fragrant. This step is important — you’re building the flavor base here, so don’t rush it.
Add the garlic and cook for about 30 seconds, just until fragrant. Stir in the tomato paste and cook it for another minute to deepen its flavor.
Sprinkle in the flour and stir constantly for about one minute. This creates a light roux that helps thicken the bisque without making it heavy.
Slowly pour in the seafood stock and chicken broth, stirring as you go to avoid lumps. Bring the mixture to a gentle simmer and let it cook for about 10 minutes, allowing the flavors to come together.
Reduce the heat to low and stir in the heavy cream and half-and-half. Add paprika, salt, black pepper, and cayenne if using. Let the soup warm gently — do not boil.
Using an immersion blender, blend the soup until smooth and silky. If using a regular blender, work in batches and return the soup to the pot.
Stir in the chopped lobster meat and sherry or brandy. Let the bisque simmer gently for another 5 to 7 minutes, just until the lobster is heated through.
Taste and adjust seasoning as needed. Serve hot, garnished with fresh herbs.