Over medium heat, combine cream and star anise. Heat until bubbles form along edge of pan. Remove from heat, cover, and let steep for 30 minutes.
Preheat oven to 325 degrees.
Remove the star anise from cream. Reheat cream until bubbles form again and remove from heat.
Combine pumpkin puree and egg yolks. Add 1/2 cup of brown sugar and the spices and beat well. Pour 1/2 cup of the hot cream into pumpkin mixture, add the remaining cream and combine. Add the vanilla.
Ladle the pumpkin custard into six custard cups and transfer cups to a baking dish. Pour in boiling water to reach halfway up the sides of the cups. Bake until custards are set in the center, about 30 minutes. Remove custards from water and let cool for 15 minutes, then re-cover and refrigerate until cold.
Preheat a broiler. Sprinkle a thin layer of the remaining brown sugar over the tops of the custards. Place them under the broiler until the sugar caramelizes, 1-2 minutes. Serve warm, or chill, uncovered, and serve cold.