Preheat the oven to 375° and line a muffin pan with paper liners or spray with non-stick cooking spray.
In a medium bowl, whisk flour, baking powder, baking soda and salt together. Set aside.
In a large bowl, mix melted butter, sugar, egg and vanilla together until combined.
Stir in flour mixture and then fold in mashed bananas and one cup of chopped walnuts.
Spoon muffin batter into the prepared muffin pan and sprinkle coarse sugar and the remaining ¼ cup of chopped walnuts on each muffin.
Bake for 20 minutes or until a toothpick inserted in the center comes out clean and the tops are golden.
Carefully remove from the oven and let sit for a couple minutes then transfer to a wire rack to cool.