Preheat your oven to 375°F (190°C) and grease a 15x10-inch jelly roll pan.

In a large mixing bowl, combine sugar, sour cream, softened unsalted butter, and eggs. Cream these ingredients on medium speed until smooth and fluffy (about 2 minutes).

Mash your very ripe bananas in a separate bowl, then add them and vanilla extract to the creamed mixture. Mix on low speed until well integrated.

In another bowl, sift together all-purpose flour, baking soda, and salt. Gradually add this dry mixture into the banana mixture, stirring gently until combined.

Fold in the chopped walnuts or other optional ingredients. Pour the batter into the greased pan and smooth the surface with a spatula.

Bake for 20 to 25 minutes, until golden brown and a toothpick inserted in the center comes out clean.

As the brownies cool, prepare the brown butter frosting by melting unsalted butter in a saucepan until golden brown with a nutty aroma.

In a mixing bowl, whisk together the browned butter, powdered sugar, vanilla extract, and milk until smooth. Adjust consistency as needed.

Spread the brown butter frosting over the cooled brownies for an extra layer of deliciousness.