Preheat the oven to 350°F and grease an 8x8 inch baking pan.

Whisk the melted butter and brown sugar together in a large bowl.

Stir in the egg, mashed bananas, and vanilla extract.

Fold in the flour until just combined.

Stir in the chopped walnuts.

Pour the batter into the pan and bake for 25 minutes until the edges pull away from the sides.