Preheat the oven to 356°F (180°C).
Grease a 9-inch round pan with butter and set aside.
Melt the butter (either in a pan or microwave) and combine with the brown sugar. Spread it evenly into the cake pan and top with sliced bananas. Set aside.
In a small bowl, mix together cake flour, all-purpose flour, coconut milk powder, salt, baking soda, and set aside.
In a large bowl, cream together the sugar and sour cream. When combined, add the coconut milk, egg, and softened butter. Add the mashed banana and coconut rum.
Add the dry ingredients into the wet ingredients and stir until just combined.
Pour the batter over the sliced bananas and bake for 30 minutes, or until a toothpick inserted comes out clean.
Let the cake cool for 10 minutes before inverting onto a plate.