Preheat oven to 375°F. Lightly spray a 12-cup muffin tin with nonstick spray or line with paper liners.
In a large bowl, stir together the oats, flour, sugar, baking powder, baking soda, salt, cinnamon, and nutmeg until combined.
In a smaller bowl, whisk together the egg, oil, and vanilla until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. The batter will look quite dry - this is normal.
Add the mashed bananas and fold into the batter until no dry pockets remain and everything is fully incorporated.
Divide the batter evenly among the 12 muffin cups.
In a small bowl, mix together the topping ingredients (oats, cinnamon, brown sugar, melted butter) until crumbly. Sprinkle evenly over each muffin.
Bake for 18–20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let cool completely before storing.