Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
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, and brown sugar. Mix well until smooth.
Add the egg, melted butter, and vanilla extract to the banana mixture. Stir until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, folding 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 allow them to cool in the pan for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.