Preheat the oven to 350°F and line a 12-cup muffin pan with paper liners.
Mash the bananas in a medium mixing bowl until mostly smooth. Add the eggs, milk, and vanilla, and whisk until well combined.
Combine the oats, baking powder, cinnamon, baking soda, and salt in a separate bowl. Stir to mix evenly.
Add the dry ingredients to the wet mixture and stir just until incorporated. Let the batter rest for 10 minutes so the oats can soften and thicken.
Divide the batter evenly between the muffin cups, filling each about ¾ full.
Bake for 20–25 minutes or until the tops are set and a toothpick inserted in the center comes out clean. Cool in the pan for a few minutes, then transfer to a rack to cool completely.