01 - Preheat the oven to 350°F. Line a 9x13-inch baking pan with parchment paper and lightly grease the surface.
02 - Whisk together melted butter and sugar in a large bowl until smooth. Add eggs one at a time, mixing thoroughly after each addition.
03 - Stir in mashed bananas and vanilla extract until evenly distributed throughout the mixture.
04 - In a separate bowl, sift together flour, baking powder, and salt to ensure even distribution.
05 - Gently fold the dry ingredients into the wet mixture until just combined. Avoid overmixing to maintain tender texture.
06 - Spread batter evenly into the prepared pan. Bake for 27–32 minutes until a toothpick inserted in the center comes out clean. Cool completely in the pan before frosting.
07 - Cook butter in a saucepan over medium heat for 4–5 minutes, swirling frequently, until golden brown with a nutty aroma. Remove from heat and cool for 5 minutes.
08 - Combine the browned butter, powdered sugar, 2 tbsp milk, vanilla extract, and salt. Beat until smooth and spreadable, adding up to 1 additional tablespoon of milk if necessary for desired consistency.
09 - Spread frosting evenly over the cooled brownies. Cut into squares and serve immediately or store in an airtight container.