Preheat the oven to 350°F (175°C). Grease or line a jumbo muffin tin with paper liners.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
In a large bowl, combine the melted unsalted butter and granulated sugar. Mix until smooth.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Stir in the vanilla extract and mashed ripe bananas until well combined.
Add the sour cream and mix until smooth.
Gradually fold the dry ingredients into the wet ingredients until just combined. Do not overmix.
Divide the batter evenly among the 6 jumbo muffin cups, filling each about 3/4 full.
Bake in the preheated oven for 22 to 25 minutes, or until a toothpick inserted into the center comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes before transferring to a wire rack to cool completely.