Preheat oven to 350 degrees F (175 degrees C). Line 12 muffin cups with paper liners.
Mash bananas in a bowl until no lumps remain. Add brown sugar, egg whites, egg, and canola oil; mix thoroughly. Stir flour, oats, baking soda, salt, and baking powder into the batter until just combined.
Fill muffin cup 2/3-full with batter.
Bake in the preheated oven until tops spring back when lightly pressed, 20 to 25 minutes.