Preheat the oven to 350°F (175°C). Line a 12-cup muffin pan with paper liners or lightly grease the cups.
Mash the ripe bananas in a large mixing bowl.
Add melted butter, granulated sugar, brown sugar, eggs, and vanilla extract. Whisk until well combined.
In a separate bowl, whisk together flour, baking soda, and salt.
Add the dry ingredients to the banana mixture and gently stir until just combined. Do not overmix.
Fold in the chopped walnuts or pecans.
Divide the batter evenly among the prepared muffin cups, filling each about three-quarters full.
Sprinkle additional chopped nuts over the tops if desired.
Bake for 18–22 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool the muffins in the pan for 5 minutes, then transfer them to a wire rack to cool before serving.