Sauté lobster head, body, and tail shells in hot oil in a large pot over high heat 2 to 3 minutes. Add onion, carrot, and celery, and sauté 3 minutes or until vegetables are tender. Stir in brandy, and cook 1 minute. Stir in tamarind paste, tomato paste, and broth. Bring to a boil, reduce heat, and simmer 45 minutes.
Process one-third of mixture in a blender or food processor until shells are coarsely chopped. Pour mixture through a wire-mesh strainer into a large saucepan, pressing down with back of a wooden spoon. Discard shells. Repeat procedure twice.
Add cream to sauce, and cook over medium-high heat until thoroughly heated. Stir in salt and hot sauce.
NOTE: If there is any extra sauce, serve with hot pasta or other grilled seafood.