Lobster shells cooked in lobster stock boosts the flavor factor in the pasta sauce.
1. Wrap star anise, peppercorns, and, if desired, lobster shells in a piece of cheesecloth, and tie with kitchen string; set aside.
2. Heat 1/4 cup butter in a large saucepan over medium-high heat. Add carrot and next 3 ingredients; cook 8 minutes or until tender.
3. Deglaze pan with cognac. Cook 10 minutes or until reduced to 1/4 cup.
4. Add lobster stock and spice bundle. Bring to a boil, reduce heat, and simmer 20 to 30 minutes or until reduced by half. Cool slightly.
5. Remove spice bundle; puree vegetable mixture in a blender until smooth. Strain mixture, and return to saucepan; cook over low heat until thoroughly heated. Remove from heat. Whisk in 1/2 cup butter.