Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, combine the mashed bananas, Greek yogurt, granulated sugar, brown sugar, and vegetable oil. Mix until smooth.
Add the eggs one at a time to the banana mixture, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, folding gently until just combined. Do not overmix.
Divide the batter evenly among the prepared 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 allow them to cool in the tin for 5 minutes. Then transfer to a wire rack to cool completely.