Preheat the oven to 375°F.
In a large bowl, mix together the oats, flour, sugar, baking powder, baking soda, cinnamon, ground nutmeg, and salt.
In a separate smaller bowl, whisk the egg, oil, and vanilla until well combined.
Pour the wet mixture into the bowl with the dry ingredients and stir until just combined. The mixture will be quite dry at this point.
Add the mashed bananas and fold them into the batter. Continue folding until all the dry ingredients are fully incorporated.
Divide the batter evenly into a muffin tin that has been lightly sprayed with nonstick spray or lined with paper liners.
In another bowl, mix the oats, cinnamon, brown sugar, and melted butter to make the topping. Sprinkle this mixture evenly over the muffin batter.
Bake in the preheated oven for 18 to 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.