01 - Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper and lightly grease.
02 - In a large bowl, whisk melted butter and sugar until smooth and well combined.
03 - Beat in eggs one at a time, ensuring each is fully incorporated. Stir in mashed bananas and vanilla extract.
04 - In a separate bowl, mix flour, baking powder, and salt. Fold dry ingredients into wet mixture until just combined—avoid overmixing.
05 - Spread batter evenly into prepared pan. Bake for 27-32 minutes until toothpick inserted in center comes out clean. Cool completely in pan.
06 - Cook butter in saucepan over medium heat until golden brown and nutty, about 4-5 minutes. Remove from heat and cool slightly for 5 minutes.
07 - Combine browned butter, powdered sugar, 2 tablespoons milk, vanilla extract, and salt. Beat until smooth and spreadable, adding up to 1 more tablespoon milk if needed.
08 - Spread frosting evenly over cooled brownies. Cut into squares and serve.