Cook lobster: Boil or steam the lobster tails for 6–8 minutes. Let cool, then remove the meat. Chop and set aside. Keep the shells.
Make flavor base: In a large pot, melt butter. Add onion, celery, carrot, and garlic. Sauté for 5–7 minutes.
Add tomato paste & flour: Stir in tomato paste, cook 1 minute. Add flour and mix well for 2 more minutes.
Add stock & lobster shells: Pour in stock and add lobster shells. Simmer uncovered for 20 minutes. Remove shells.
Blend & strain: Use an immersion blender (or regular blender) to puree. Strain through a fine mesh sieve for smooth texture.
Finish the bisque: Return soup to pot. Stir in cream and sherry. Add chopped lobster meat. Simmer on low for 5 more minutes. Season with salt and pepper.
Serve: Garnish with fresh herbs. Serve hot with crusty bread.