Rinse lobster shells and crush. Peel the onion. Rinse leek, celery and carrots. Cut vegetables into chunks.
Heat butter in a pan and saute lobster until it darkens slightly. Add vegetables and saute briefly. Add the tomato paste, thyme and parsley and deglaze with cognac. Add the white wine and enough water to cover contents (about 1 liter) (approximately 4 cups). Add the bay leaves, pepper and fennel seeds and bring to boil. Skim off the foam from the surface. Reduce heat and simmer for about 30 minutes. Strain broth through a sieve lined with cheesecloth, discarding solids.
Use the lobster stock to make soups and sauces.