Preheat oven to 220°C. Roast lobster shells 15 minutes until bright red and fragrant.
Melt butter and oil in large pot. Sauté onion, celery, carrot, and garlic 10 minutes.
Add tomato paste, cook 3 minutes. Add roasted shells.
Pour in Cognac and flambé carefully (or simmer to evaporate). Add white wine, reduce by half.
Add fish stock, cayenne, paprika, and tarragon. Simmer 30 minutes.
Strain through a fine sieve, pressing shells firmly. Discard solids.
Add heavy cream to strained broth. Simmer 10 minutes. Season well.
Dice reserved lobster meat. Ladle bisque into warm bowls, top with lobster pieces and fresh tarragon.