Combine the milk and star anise in a small, heavy saucepan. Heat to 180° or until tiny bubbles form around edge of pan, stirring frequently (do not boil). Remove from heat; cover and steep 20 minutes. Strain milk mixture through a fine sieve into a large bowl; discard star anise. Add 1/2 cup sugar, ginger, cinnamon, and eggs; stir with a whisk. Gently stir in bread. Let stand 10 minutes, stirring occasionally.
Preheat oven to 350°.
Pour into an 8-inch square baking dish coated with cooking spray. Sprinkle the mixture evenly with 1 tablespoon sugar. Bake at 350° for 35 minutes or until a knife inserted in center comes out clean. Serve each piece warm with 1/4 cup ice cream.