Preheat oven to 350 degrees F. Spray a muffin tin pan with cooking spray, or use with muffin paper liners.
In a large bowl, mix together flour, baking soda, baking powder, and salt. In another bowl, beat together bananas, white sugar, brown sugar, egg, vanilla, and melted butter. Stir the banana mixture into the flour mixture just until moistened. Stir in the chopped nuts. Spoon batter into prepared muffin cups. (I use an ice cream scoop to scoop just the right amount of batter in each tin and to get nice rounded muffin tops.)
Bake in preheated oven for about 20 minutes, or until a toothpick inserted into center of a muffin comes out clean.