Place a heavy bottomed ten-quart pot over high heat. Add olive oil. When the oil is smoking, add the bodies, onions, celery, carrots and garlic. Stir frequently until onions are translucent. Add cayenne, paprika, tomato paste, thyme, and pickling spice. Add brandy, sherry, reserved lobster broth, lobster base (if available) and bring to a boil and simmer for 40 to 60 minutes. Add roux to the liquid using a wire whisk and then simmer for 10 minutes.