Preheat your oven to 350°F (175°C). Grease a muffin tin or line with muffin liners.
In a large bowl, mix together the oats, flour, brown sugar, baking powder, baking soda, and salt.
In another bowl, combine the mashed bananas, beaten egg, melted butter, and vanilla extract.
Add the wet ingredients to the dry ingredients and stir until just combined. Do not overmix.
Divide the batter evenly among the muffin cups.
Bake for 20 minutes or until a toothpick inserted into the center of a muffin comes out clean.
Allow muffins to cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.