Preheat oven to 350°F (175°C). Grease or line a muffin tin for 2 muffins.
Mash the banana in a bowl.
Mix dry ingredients: In another bowl, combine flour, baking powder, baking soda, and salt.
Whisk wet ingredients: In a third bowl, beat the egg, sugar, melted butter, and vanilla.
Combine: Add the mashed banana to the wet mix, then stir in the dry ingredients. Mix gently.
Fill muffin tin: Pour the batter evenly into 2 muffin cups, about 3/4 full.
Bake for 18-20 minutes, or until a toothpick comes out clean.
Cool: Let the muffins cool in the tin for a few minutes, then transfer to a rack to cool completely.