Preheat oven to 350℉ (175℃). Grease a muffin pan with baking spray or line it with cupcake liners, and set aside.
Whisk the eggs, mashed bananas, sugar (brown and white), sour cream, and vanilla extract in a small bowl.
In another bowl, combine flour, baking powder, baking soda, and salt.
Gradually add the wet ingredients to the dry ingredients and mix well.
Finally, pour the melted butter in and gently mix it, scraping down the sides as you go.
Pour the muffin batter into the prepared pan and bake for about 20 minutes. If using a loaf pan, it may take an hour or more to bake. Either way, a toothpick inserted in the center will come out clean.