Preheat your oven to 375°F (190°C) and grease a 9x13 inch baking pan.

Combine granulated sugar, sour cream, softened butter, and eggs in a mixing bowl using an electric mixer.

Add mashed bananas and vanilla extract to the mixture and mix until fully incorporated.

Gradually add flour, baking soda, and salt; stir gently until just combined.

Fold in the chopped walnuts and distribute evenly.

Pour the batter into the pan and bake for 20-30 minutes, checking doneness with a toothpick.

Allow to cool in the pan for 15-20 minutes, then transfer to a wire rack.

For the frosting, melt butter until golden, then whisk in powdered sugar, milk, and vanilla.

Spread the frosting over cooled brownies and let set before cutting into squares.