Preheat oven to 350°. If you have a convection oven, use this setting.
Grease 36 non-stick mini muffin tins with cooking spray. Or bake them in batches, be sure to grease each time you use the pan.
In a small bowl, mash the bananas. Set aside.
In a medium bowl, combine flour, baking soda, salt, zest and cinnamon. Set aside.
In a large mixing bowl, cream butter and sugar with a wooden spoon. (Not enough batter to drag out the mixer). Add eggs, vanilla, rum, apple sauce and bananas.
Add flour mixture and combine just until mixed. Do not over-mix.
With a tablespoon (or I use a small ice cream scoop), drop about 3/4 T. of banana mixture into the muffin tins until 3/4 full.
Bake for about 10-13 minutes until done and a toothpick inserted in the center comes out clean.
Cool in pan for about 3-5 minutes. Then transfer to a wire rack.
Mix topping ingredients together. Microwave just until butter is melted. Stir well.
Drizzle topping over warm muffins.