Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or lightly grease with cooking spray.
In a large mixing bowl, combine the mashed bananas, egg, unsweetened applesauce, whole milk, and vanilla extract. Mix well until smooth.
In a separate bowl, whisk together the whole wheat flour, baking soda, baking powder, ground cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients and stir until just combined. Do not overmix.
Spoon the batter evenly into the prepared muffin cups, filling each about 3/4 full.
Bake for 18 to 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before serving.