Preheat oven to 375°F (190°C). Grease a muffin tin or line with muffin liners.
In a large bowl, combine the oats, flour, baking powder, baking soda, and salt.
In another bowl, mix the mashed bananas, egg, brown sugar, melted butter, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Divide the batter evenly among the muffin cups.
Bake for 20 minutes or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.