01 - Preheat oven to 350°F. Line a 9x13-inch baking pan with parchment paper and lightly grease the surface.
02 - In a large bowl, whisk together melted butter and granulated sugar until smooth and fully incorporated.
03 - Beat in eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in mashed bananas and vanilla extract until uniform.
04 - In a separate bowl, combine all-purpose flour, baking powder, and salt. Whisk to ensure even distribution.
05 - Fold dry ingredients into the wet mixture until just combined. Do not overmix—small lumps are acceptable.
06 - Spread batter evenly in the prepared pan. Bake for 27-32 minutes until a toothpick inserted in the center comes out clean. Cool completely in the pan.
07 - In a saucepan over medium heat, cook butter until golden brown with a nutty aroma, approximately 4-5 minutes. Remove from heat and cool for 5 minutes.
08 - Combine browned butter, powdered sugar, 2 tablespoons milk, vanilla extract, and salt. Beat until smooth and spreadable, adding additional milk if needed to achieve desired consistency.
09 - Spread frosting evenly over cooled brownies. Cut into 16 squares and serve immediately or store in an airtight container.