In a large bowl, add the browned butter, applesauce, and both sugars: mix with a hand mixer to combine. Add eggs and mix first on low speed, then on high speed until mixture is well combined and smooth. Add bananas and mix until smooth again. Add molasses, vanilla, cinnamon, whole wheat flour, and baking powder (stir on top of flour), then mix until smooth again. Add remaining ingredients and stir to combine, but do not overmix. There should be no dry spots in batter.