Prepare Lobster and Stock: If using live lobsters, cook them in boiling salted water for 8–10 minutes until shells are bright red. Remove lobster meat and reserve shells. Chop meat into bite-sized pieces.
Make Lobster Stock: In a large pot, melt 2 tablespoons butter. Sauté lobster shells, onion, celery, carrots, and garlic for 5–7 minutes. Add tomato paste, paprika, thyme, and cayenne; cook for 2 minutes. Add wine and simmer until reduced by half. Pour in lobster or seafood stock and simmer 20 minutes. Strain stock and discard solids.
Prepare Bisque Base: Melt remaining butter in a clean pot. Gradually whisk in strained stock. Simmer gently for 10 minutes.
Add Cream and Sherry: Reduce heat to low. Stir in heavy cream and sherry. Simmer gently for 5 minutes; do not boil to avoid curdling.
Add Lobster Meat: Fold in chopped lobster meat. Simmer 3–5 minutes until heated through.
Season and Serve: Taste and adjust seasoning with salt and pepper. Ladle bisque into bowls and garnish with fresh chives or parsley.