Preheat oven to 350°.
Combine granulated sugar and water in a small heavy saucepan, and cook over medium heat 8 minutes or until golden, stirring gently. Immediately stir in anise extract; pour into a 6 1/2-cup metal ring mold coated with cooking spray, tipping quickly until caramelized sugar coats bottom of pan. Set aside.
Combine Pumpkin Pureé and brown sugar in a blender or food processor, and process until smooth. Add cornstarch and next 5 ingredients (cornstarch through egg white); process until smooth. Add milk, rum, and vanilla; process until smooth. Pour into mold, and cover with foil. Place mold in a 13 x 9-inch baking pan; add hot water to pan to a depth of 1 inch.
Bake flan at 350° for 1 hour or until a knife inserted in center comes out clean. Remove mold from pan, and cool, uncovered, on a wire rack. Cover and chill at least 3 hours.
Loosen edge of flan with a knife or rubber spatula. Place a plate upside down on top of mold; invert flan onto plate. Drizzle any remaining caramelized syrup over flan. Garnish with star anise, if desired.
Note: If you don't have a 6 1/2-cup ring mold, substitute a 9-inch round cake pan.
Note: Anise extract can be found in the spice section of your local supermarket.