Add the rolled oats to a large mixing bowl and pour the milk over the oats.
Stir gently until combined and let the oats soak for 10 minutes to soften.
While the oats soak, whisk the flour, baking soda, baking powder, salt, and cinnamon together in a separate bowl.
In another bowl, mash the bananas until mostly smooth with small lumps remaining.
Add the oil, brown sugar, egg, and vanilla to the mashed bananas and whisk until smooth and cohesive.
Stir the soaked oats once, then add the banana mixture to the oat bowl and mix gently.
Add the dry ingredients to the wet mixture and fold slowly with a spatula until no dry streaks remain.
Let the batter rest for 5 minutes to allow the oats to fully hydrate.
Preheat the oven to 375°F while the batter rests.
Line a standard 12-cup muffin pan with paper liners or lightly grease the cups.
Scoop the batter evenly into the muffin cups, filling each about ¾ full.
Place the muffin pan on the center rack of the oven.
Bake for 18 to 22 minutes until the tops are lightly golden and spring back when pressed.
Insert a toothpick into the center of a muffin; it should come out clean or with a few moist crumbs.
Remove the muffins from the oven and let them cool in the pan for 5 minutes.
Transfer the muffins to a wire rack to cool completely before storing or serving.