01 - Preheat the oven to 350°F (175°C). Grease a 9x9-inch cake pan and line it with parchment paper.
02 - Melt the butter in a saucepan over medium heat, stirring frequently, until it foams and turns golden brown with a nutty aroma, about 5–7 minutes. Transfer immediately to a bowl and let cool slightly.
03 - In a medium bowl, whisk together the flour, baking soda, cinnamon, and salt. Set aside.
04 - In a large bowl, beat the browned butter and granulated sugar together until creamy and well combined.
05 - Add the eggs one at a time, mixing thoroughly after each addition until fully incorporated.
06 - Fold in the mashed bananas, sour cream, and vanilla extract, mixing until the mixture is smooth and uniform.
07 - Gradually fold the dry ingredient mixture into the wet batter until just combined. Be careful not to overmix.
08 - Pour the batter into the prepared cake pan and smooth the top with a spatula.
09 - Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean.
10 - Let the cake cool completely in the pan on a wire rack before frosting.
11 - Beat the softened cream cheese and butter together until smooth and fluffy. Gradually add the sifted powdered sugar, vanilla extract, and a pinch of salt, beating until thick and creamy.
12 - Spread the cream cheese frosting generously over the cooled cake. Slice into squares and serve.