Preheat the oven to 350 degrees F (175 degrees C). Grease a 12-cup muffin tin or line cups with paper liners. Sift flour, baking powder, baking soda, and salt together in a bowl; set aside.

Mix bananas, sugar, egg, and melted butter in a separate large bowl until well combined; fold in flour mixture until smooth. Spoon batter into the prepared muffin cups, filling each 2/3 full.

Bake in the preheated oven until tops spring back when lightly pressed, about 25 to 30 minutes. Cool briefly in the tin, then transfer to a wire rack to cool completely.