Preheat the Oven: Preheat the oven to 400°F.
Prepare the Muffin Pan: Line a 12-cup muffin pan with 12 muffin liners.
Mash the Bananas: Place the very ripe bananas in a large bowl and mash them until only small chunks remain.
Combine the Wet Ingredients: Add the melted and cooled butter and packed brown sugar to the mashed bananas. Stir until well combined, then mix in the lightly beaten eggs and vanilla extract until incorporated.
Add the Dry Ingredients: Add the flour, baking soda, baking powder, and salt to the banana mixture. Stir gently just until the ingredients are combined, taking care not to overmix the batter.
Fold in the Nuts: Gently fold the chopped walnuts and/or pecans into the batter until they are evenly distributed and just combined.
Fill the Muffin Cups: Divide the batter evenly among the 12 prepared muffin cups.
Add Optional Nut Topping: If desired, sprinkle additional chopped nuts over the tops of the filled muffin cups. Lightly press the nuts into the batter so they stay in place while remaining visible on top.
Adjust the Oven Temperature: Place the muffin pan in the 400°F oven, then immediately reduce the oven temperature to 350°F.
Bake the Muffins: Bake for approximately 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean and the tops are beginning to turn golden brown.
Cool Briefly: Remove the pan from the oven and let the muffins cool for 5 minutes.
Remove and Serve: Carefully remove the muffins from the pan and serve.