Line a loaf pan with parchment paper or spray it with cooking spray.
Combine the milk and vinegar and let the mixture sit for 5 minutes.
Mash the bananas until smooth.
Add the sugar, applesauce, vanilla, and milk/vinegar mixture to the bananas.
Combine the flour, baking soda, cinnamon, and allspice.
Mix the banana mixture into the dry ingredients, then stir in the nuts.
Pour the banana bread batter into the prepared pan and bake it for 50 to 60 minutes, or until a toothpick comes out clean when inserted into the center of the loaf.