Preheat your oven to 375°F (190°C). Grease a 15x10-inch jelly roll pan with butter and dust with flour.

In a large mixing bowl, cream together sugar, sour cream, and softened butter with an electric mixer on medium speed for about 2 minutes until smooth.

Add eggs one at a time, mixing until well combined.

Mash ripe bananas in a separate bowl, then add to the creamy mixture along with vanilla extract and blend on low speed for 1 minute.

In another bowl, sift flour, baking soda, and salt. Gradually add to the banana batter, mixing gently until just combined.

Fold in chopped walnuts (if using), then pour mixture into prepared pan, spreading evenly.

Bake for 20-25 minutes until golden brown and a toothpick comes out clean. Cool in the pan for 10 minutes.

For the frosting, melt butter in a saucepan over medium heat until golden brown, about 5-7 minutes. Allow to cool slightly.

Whisk browned butter with sifted powdered sugar, vanilla extract, and milk until smooth and creamy.

Spread frosting over cooled brownies and enjoy!