Preheat your oven to 375°F (190°C). Grease and flour a 15x10-inch jelly roll pan or line it with parchment paper.

In a large mixing bowl, combine sugar, sour cream, softened butter, and eggs using an electric mixer. Beat on medium speed until creamy, about 2-3 minutes. Fold in mashed bananas and vanilla extract.

In another bowl, whisk together all-purpose flour, baking soda, and a pinch of salt. Gradually add the dry mixture to the wet ingredients, mixing gently.

If using, fold in walnuts or substitute with chocolate chips.

Pour the brownie batter into the prepared pan and spread evenly. Bake for 20-25 minutes, or until golden brown.

In a saucepan, melt the butter over medium heat until it bubbles and turns golden brown. Stir constantly to prevent burning.

Remove from heat and whisk in powdered sugar, vanilla extract, and milk until smooth and creamy.

Spread the warm brown butter frosting evenly over the brownies while they are still warm.

Allow the brownies to cool completely in the pan before slicing into squares.