Combine white whole wheat flour, baking powder, baking soda, and salt. Set aside.
Whisk applesauce, milk, sugar, vanilla, and egg until well combined.
Gently add bananas to wet ingredients. Fold flour mixture into wet ingredients, just until combined.
Divide muffin batter among 12 lined muffin tins. Bake 18-20 minutes, until cooked through.