Preheat the oven to 350°F. Grease and line an 8x8 or 9x9-inch baking pan with parchment paper.
In a large mixing bowl, whisk together the browned butter, brown sugar, and granulated sugar until combined.
Add the mashed bananas, eggs, sour cream, and vanilla extract. Mix until smooth.
Add the flour, baking soda, salt, and cinnamon. Stir until just combined. Do not overmix.
Pour the batter into the prepared pan and smooth the top evenly.
Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely.
While the cake cools, make the salted caramel. Heat the sugar in a saucepan over medium heat until melted and amber in color.
Stir in the butter until fully combined. Slowly pour in the heavy cream while stirring carefully. Remove from the heat and stir in the salt. Let cool.
In a mixing bowl, beat together the butter and cream cheese until smooth.
Add the powdered sugar, vanilla extract, and salt. Beat until light and fluffy.
Spread the frosting over the cooled cake.
Drizzle the salted caramel over the frosting and gently swirl for a marbled effect.
Sprinkle with flaky sea salt or chopped nuts if desired, then slice and serve.