Preheat oven to 350º F. Spray an 8x4" loaf pan with nonstick cooking spray. In a bowl, sift to combine flour, baking soda, baking powder, salt and cinnamon (if using). Set aside. In a separate bowl, combine applesauce, sugar and bananas. Mix well. Add eggs, milk and vanilla. Gradually stir in dry ingredients. Stir only until JUST combined. DO NOT OVER MIX. If using, fold in nuts.
Transfer to loaf pan and then to the oven.
Bake for 60-64 minutes, or until toothpick inserted comes out clean. Let cool in pan for 10 minutes, then transfer to cooling rack.