01 - Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper and lightly grease.
02 - Whisk melted butter and sugar in a large bowl until smooth.
03 - Beat in eggs one at a time, mixing well after each addition. Stir in mashed bananas and vanilla extract.
04 - In a separate bowl, whisk together flour, baking powder, and salt.
05 - Fold dry ingredients into wet mixture until just combined. Spread batter evenly into prepared pan.
06 - Bake for 27-32 minutes until a toothpick inserted in center comes out clean. Cool completely in pan.
07 - Cook butter in a saucepan over medium heat for 4-5 minutes until golden brown with nutty aroma. Cool for 5 minutes.
08 - Combine browned butter, powdered sugar, 2 tablespoons milk, vanilla extract, and salt. Beat until smooth and spreadable, adding more milk if needed.
09 - Spread frosting over cooled brownies. Cut into squares and serve.