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 Pure 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.