Pre-heat the oven to 375°F.
Grease a 9-inch x 13-inch baking pan with non-stick cooking spray.
In a mixing bowl, using an electric mixer, mix together sugar, sour cream, softened butter and eggs; beat until well combined.
Add mashed bananas and vanilla extract; mix until combined.
Add the dry ingredients (all-purpose flour, baking soda and salt) to the batter; mix until combined.
Add the chopped walnuts; gently mix to combine.
Pour the banana batter into the prepared baking pan.
Place in the pre-heated oven and bake for 20 to 30 minutes or until baked; check the readiness of the Banana Bread Brownies, using a toothpick, inserted in the center; if it comes out clean, the brownies are ready.
Remove the baking pan from the oven; allow to cool slightly.
While the brownies are cooling, prepare the frosting.
In a saucepan, melt butter and heat until medium brown color.
Turn off the heat and add confectioners' sugar, 1 cup at a time; stir until combined after each addition.
Add milk and vanilla extract; mix until combined.
Pour the frosting over the brownies; spread evenly.
Allow the Banana Bread Brownies to cool completely; cut and serve.
