Preheat oven to 350 degrees. Spray (2) 5.75X3.25x2.25 or (1) 8 inch loaf pan with nonstick cooking spray. Line the bottom with parchment paper and spray that.
In a microwave safe bowl, microwave butter for 30 seconds or until melted.
In a large mixing bowl, add in the brown bananas. Mash them thoroughly using a fork. Add in the melted butter, granulated and brown sugar, eggs, rum, and vanilla.
Mix on medium until everything is combined.
Add in the flour and baking soda and mix on low until the flour is somewhat incorporated. Bump the mixer up to medium and mix until combined.
Divide the batter in half and place it in the 2 mini loaf pans or put all the batter in 1 8 inch loaf pan.
Bake mini loaves for 40-45 minutes or until it's done. The 8 inch will take 1 hour and 8-10 minutes. Place a toothpick in the middle of the loaf and if it comes out clean or with a few small crumbs on it, it's done. If there is still batter on the toothpick, give it a few more minutes and test it again.
Let cool in the pan for 10 minutes and then turn out onto a cooling rack to finish cooling.