01 - Preheat oven to 350°F. Grease a 9x9-inch baking pan and line with parchment paper, leaving overhang on two sides for easy removal.
02 - Melt butter in a medium saucepan over medium heat, stirring frequently. Continue cooking until the butter foams, turns a golden amber color, and releases a nutty aroma, about 5 to 7 minutes. Immediately transfer to a mixing bowl and let cool slightly.
03 - In a medium bowl, whisk together the all-purpose flour, baking soda, ground cinnamon, and salt until evenly distributed.
04 - In a large bowl, beat the browned butter with the granulated sugar using an electric mixer until creamy and well incorporated.
05 - Add the eggs one at a time, beating thoroughly after each addition until the mixture is smooth and emulsified.
06 - Fold in the mashed bananas, sour cream, and vanilla extract, mixing until the batter is smooth and uniform.
07 - Gradually add the dry ingredient mixture to the wet batter, folding gently with a spatula until just combined. Avoid overmixing to keep the cake tender.
08 - Pour the batter into the prepared baking pan and use a spatula to smooth the surface evenly.
09 - Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean and the top is golden.
10 - Allow the cake to cool completely in the pan set on a wire rack before applying frosting.
11 - In a mixing bowl, beat the softened cream cheese and butter together with an electric mixer until light and fluffy. Gradually add the sifted powdered sugar, vanilla extract, and a pinch of salt, beating until the frosting is thick and creamy.
12 - Spread the cream cheese frosting generously over the completely cooled cake. Slice into squares and serve.