Preheat the oven to 350 degrees F (175 degrees C). Grease a 12-cup muffin tin or line cups with paper liners.

Combine bananas, melted butter, egg, and vanilla extract in a bowl. Sift in brown sugar. Mix well and set aside.

Sift all-purpose flour, whole wheat flour, baking powder, baking soda, cinnamon, nutmeg, and salt into a separate bowl. Slowly fold flour mixture into the banana mixture, being careful not to overmix.

Scoop batter evenly into the muffin cups.

Bake in the preheated oven until tops spring back when lightly pressed, 20 to 27 minutes. Remove from the muffin tin and let cool.