Preheat oven to 350 degrees F. Prepare a 9 X 5-inch bread pan by spraying it on the bottom and less than halfway up on the sides with cooking spray or by greasing it with butter.
In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, salt and nutmeg.
In a medium bowl, lightly beat the eggs. Mix in the banana and sugar.
In a medium skillet over medium heat, melt the butter. Once the butter is melted add the rum to the pan. Continue to cook while stirring constantly. Remove from heat when you see golden bits of butter in the bottom of the pan. Butter / rum will continue to cook slightly once removed, so you don't want it to become too dark while on the stove. You could end up with burnt butter and burnt butter doesn't taste good in anything. The alcohol in the rum will burn off and you will see the butter foam as it cooks. Just continue to gently stir and stay focused on making sure the butter becomes golden to slightly amber in color. This will probably take 5 - 7 minutes. Lower the heat if you feel it is cooking too fast.
Add butter / rum mixture to banana mixture and thoroughly incorporate.
Add banana mixture all at once to dry ingredients and stir until just mixed. Don't worry, there will probably be some lumps. No biggie.
Bake for 55 - 60 minutes or until a toothpick inserted into the middle comes out clean.
If desired, cover loaf with some tin foil in the last 15 minutes of baking should it begin to darken too much.
Remove from oven and place pan on wire rack to cool for 15 minutes.
Remove the bread from pan and allow to cool completely on the rack.
The bread slices best once it has been wrapped in plastic wrap and left to sit overnight.