Preheat the oven to 350 degrees F (175 degrees C). Grease a muffin tin.

Sift flour, baking powder, baking soda, cinnamon, salt, and nutmeg together in a small bowl.

Mash bananas in a large bowl. Mix in white sugar, melted butter, brown sugar, egg, and vanilla extract. Fold in flour mixture until just combined. Fold walnuts into the batter.

Divide batter evenly among the prepared muffin cups.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 20 minutes.