Preheat the oven to 375 degrees. Line a muffin tin with 12 paper liners.
In a large bowl cream the butter and sugar together.
Add in the eggs and mix well. Stir in the rum and vanilla.
Mash the bananas and then add them to the sugar mixture.
In a medium bowl combine the flours, baking powder, and salt. Add the flour mixture to the sugar mixture and stir until well combined.
Stir in the cinnamon chips.
Pour the muffin mixture into the prepared muffin pans. Sprinkle each muffin with brown sugar.
Bake for 18-20 minutes or until a toothpick inserted into the center comes out clean. Cool on a wire rack.