Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a large mixing bowl, combine the mashed bananas, plain Greek yogurt, eggs, brown sugar, vegetable oil, and vanilla extract. Mix until smooth and well combined.
In a separate bowl, whisk together the rolled oats, all-purpose flour, baking powder, baking soda, ground cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
Bake in the preheated oven for 18 to 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the tin for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.