1. Preheat oven to 375°F (190°C). Grease and flour a 9×13-inch baking dish.
2. In a large bowl, cream together the butter and sugar until light and fluffy.
3. Beat in the eggs, one at a time, then stir in the sour cream and vanilla extract.
4. Combine the flour, baking soda, and salt; gradually stir into the butter mixture until well blended.
5. Fold in the mashed bananas.
6. Spread the batter evenly into the prepared baking dish.
7. Bake for 20 to 25 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool completely in the pan on a wire rack.

For the Frosting:

1. In a medium saucepan, heat the butter over medium heat until boiling. Let the butter turn a delicate brown and remove from heat immediately.
2. Pour the butter into a bowl and add the powdered sugar, vanilla extract, and milk. Beat until smooth and creamy.
3. Spread the frosting over the cooled brownies before cutting into squares.