Preheat oven to 350°F (175°C). Grease and flour a 9×13-inch baking dish or line with parchment paper.

In a large mixing bowl, cream together sugar, sour cream, and softened butter until light and fluffy.

Beat in eggs, mashed bananas, and vanilla extract until smooth.

In a separate bowl, whisk together flour, baking soda, and salt.

Gradually add dry ingredients to the wet mixture, mixing just until combined.

Fold in walnuts, if using.

Pour batter into the prepared pan and spread evenly.

Bake for 25–30 minutes, or until a toothpick inserted in the center comes out clean.

Let cool in the pan on a wire rack.

In a small saucepan, melt butter over medium heat and cook until it turns a light golden brown and smells nutty (about 4–5 minutes).

Remove from heat and let cool slightly.

Whisk in powdered sugar, vanilla, and milk until smooth and spreadable.

Spread frosting over cooled brownies.

Cut into squares or bars and serve.