Preheat the oven to 350 F. Spray a 11x7 rectangle baking dish with non stick spray.
In a bowl, combine flour, cornmeal, coconut, baking powder, nutmeg, ginger, cinnamon and star anise. Stir to combine and set aside.
In the bowl of an electric mixer, combine butter, salt and sugar.
Mix for a few minutes until well blended and creamy.
Add vanilla and eggs, one at a time, mixing until thoroughly combined, after each egg.
Add bananas, evaporated milk, coconut milk and rum. Mix until thoroughly combined.
Transfer to prepared baking dish.
Bake for 1 hour, until a tester inserted comes out clean.