Preheat oven to 350 degrees and line a loaf pan with parchment paper.
In a medium bowl with a hand mixer, combine the butter and brown sugar until smooth.
Next, add the eggs, apple sauce, bananas, and vanilla to the bowl and mix until there are no banana lumps. You can also mash up the bananas before adding to the bowl based on how ripe they are.
Add in the rest of the dry ingredients: flour, baking soda, cinnamon, nutmeg, and salt until a rich batter forms.
Fold in the walnuts to the batter then transfer the mixture to the prepared baking pan.
Cook the banana bread low and slow at 350 for 1 hour.