Preheat your oven to 375°F (190°C) and prepare a 9x13 inch baking pan by greasing it.

Combine sugar, sour cream, softened butter, and eggs in a large mixing bowl. Beat for 2–3 minutes until creamy.

Incorporate the mashed bananas and vanilla extract into the wet mixture. Mix on low speed until combined, about 1–2 minutes.

In a separate bowl, whisk together all-purpose flour, baking soda, and salt. Gradually sift into the wet ingredients and stir gently until just combined.

Gently fold in the chopped walnuts with a spatula until evenly distributed.

Pour the batter into the prepared baking pan and spread evenly. Tap the pan lightly to remove air bubbles.

Bake for 20–30 minutes, checking for doneness around the 20-minute mark. Use a toothpick to test.

Let the brownies cool in the pan for about 10 minutes.

To make the frosting, melt butter over medium heat until light golden brown, then mix in powdered sugar and milk until smooth.

Pour the frosting over the cooled brownies, spreading evenly. Allow to cool completely before slicing.