Preheat your oven to 350°F (175°C). Line a 9x13-inch pan with parchment paper or lightly grease and flour it. Set it aside.

In a large bowl, mix the softened butter with both the granulated and light brown sugars until the mixture is smooth and creamy. 

Add each egg separately, beating well after each to achieve a smooth mixture.

Incorporate the sour cream, mashed bananas, and vanilla extract until the batter is velvety and smooth, resulting in a rich texture.

In a separate bowl, whisk together the flour, baking soda, and salt to ensure everything is evenly mixed. 

Carefully incorporate the dry ingredients into the wet mixture, stirring just enough to combine and preserve the batter's texture. If you’re using chopped walnuts, stir them in now for that extra bit of crunch.

Pour the batter carefully into the pan, then spread it evenly for a consistent, smooth layer. Bake for 25 to 30 minutes, checking with a toothpick in the center, and ensure the edges are just starting to detach from the pan.

Allow the brownies to cool for a few minutes while you prepare the frosting. Start by melting the butter in a saucepan over medium heat. Mix in the brown sugar and let it cook for about 2 minutes, or until it starts bubbling.

As soon as it releases a nutty, caramel aroma, remove from the heat and blend in the powdered sugar, vanilla extract, and milk until the frosting is smooth and pourable.

Spread the freshly made frosting over the warm brownies with a spatula, creating a smooth, even layer. 

If you like, sprinkle more chopped walnuts on top for a little texture. 

Let it all set for a few minutes, then slice and serve while they’re warm!