Preheat oven to 375 degrees F and lightly butter 2 muffin tins. You may also use paper cups if desired.
In a large bowl, combine the flour, baking powder and salt, then set aside.
Add the sugar, melted butter, eggs, and vanilla – then beat well, scraping down the sides of the bowl once or twice.
Fold in the dry ingredients just until incorporated. Add the nuts and the mashed bananas with a rubber spatula. Spoon the batter into the muffin tins to fill them about ¾ of the way. Remove air bubbles by rapping the tin on the counter.
Bake for 18 to 20 minutes. Let cool before turning the muffins out.