Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a large bowl, combine 1 1/2 cups old fashioned oats, 1 cup all-purpose flour, 1 teaspoon baking powder, 1/2 teaspoon baking soda, 1/2 teaspoon salt, and 1 teaspoon ground cinnamon. Stir until well mixed.
In a separate medium bowl, mash 2 large ripe bananas with a fork until smooth.
Add 1/2 cup granulated sugar, 1/4 cup packed light brown sugar, 1/3 cup vegetable oil, 2 large eggs, 1 teaspoon vanilla extract, and 1/2 cup plain yogurt to the mashed bananas. Whisk together until combined.
Pour the wet ingredients into the dry ingredients. Stir gently with a spatula until just combined. Do not overmix; the batter should be slightly lumpy.
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.