Preheat your oven to 325 degrees and prepare a 9x13 light metal colored pan. Spray it with non-stick spray and line it with parchment paper.
Start by browning your butter. I brown both cups at once and then measure out just 1 cup for the bread and use the other for frosting.
Place a medium-sized saucepan on the stove over medium-high heat. Put in 2 cups of butter, allow them to melt down, and then boil. Monitor the butter as it boils. Once the butter stops making popping noises, stir it and ensure you see brown flecks. Remove from the heat quickly so that it doesn't burn.
In a large mixing bowl, mash the bananas until completely mushy. I like to use a potato masher to do this.
Add 2 cups of granulated sugar to the bananas, stir to combine.
Add 1/2 cup of sour cream, 3 eggs, 2 tsp of flour, and 1 cup of the browned butter. Mix to combine.
Pour in the 3 cups of all-purpose flour, 2 tsp of baking soda, 1 tsp ground cinnamon, and 1/2 tsp of fine sea salt. Mix until a batter forms.
Pour the batter into the prepared pan.
Place it in the oven and bake for 35 minutes. Once done, remove and allow the cake to cool before frosting it.
Frosting
In a standing mixer with the paddle attachment, add the 1 cup of browned butter that you set aside. Add in the 4 ounces of cream cheese and mix until combined.
Pour in 4 cups of powdered sugar and 1 tsp of vanilla. Mix until a frosting forms.
Turn the mixer on high and whip for 2 minutes.
Frost the cooled cake with the browned butter cream cheese frosting.