Preheat oven to 400 degrees. Combine first 6 ingredients in a large bowl. Whisk milk, applesauce, and vanilla to blend in medium bowl. Add milk mixture to dry ingredients, stirring until just combined. Mix in bananas. Divide batter among twelve muffin cups. Bake until toothpick inserted into center of muffins comes out clean, about 20 minutes. Transfer to rack to cool. Serve warm or at room temp.