Preheat oven to 350°F and grease an 8x8 baking pan.
Whisk melted butter and brown sugar together until smooth.
Add egg, vanilla, and mashed banana, stirring until combined.
Fold in flour, baking powder, baking soda, and salt. Mix just until no streaks remain.
Stir in walnuts or chocolate chips if using.
Spread the batter evenly into the prepared pan.
Bake for 25–30 minutes or until a toothpick inserted comes out mostly clean.
Cool completely before cutting into squares and serving.