Preheat the oven to 375°F and grease a 13x9 inch pan.

Make the brownie: In a large bowl, mix together sugar, sour cream, butter, and eggs until creamy, add the mashed bananas and vanilla extract.

Add flour, baking soda, salt, and walnuts and blend for 1 minute.

Pour the batter into the pan and bake for 25 minutes or until golden brown.

Make the frosting: make the brown butter, heat butter in a large saucepan over medium heat, and until it reaches a medium brown color turn off the heat. Add the powdered sugar, vanilla, and milk.

Pour the frosting over the banana bread brownies, and spread with a spatula. Cool completely before cutting and serving.