01 - Melt the butter in a saucepan over medium heat. Continue cooking, swirling occasionally, until the butter foams and golden-brown bits form at the bottom of the pan, about 5 to 7 minutes. Pour the browned butter into a bowl and let it cool for 10 minutes.
02 - Preheat the oven to 350°F. Grease a 9-inch round cake pan or a loaf pan and line it with parchment paper.
03 - In a medium heavy-bottomed saucepan, heat the sugar over medium heat, stirring constantly until completely melted and deep amber in color. Carefully add the cubed butter — it will bubble vigorously — and whisk until melted. Slowly drizzle in the heavy cream while whisking continuously. Remove from heat and stir in the flaky sea salt. Let the caramel cool to room temperature.
04 - In a medium bowl, whisk together the all-purpose flour, baking soda, and sea salt. Set aside.
05 - In a large bowl, combine the cooled browned butter, granulated sugar, and packed light brown sugar. Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract, mashed bananas, and sour cream until the mixture is smooth and well blended.
06 - Add the dry ingredient mixture to the wet ingredients. Fold gently with a spatula just until combined — be careful not to overmix.
07 - Spread half of the batter into the prepared pan. Drizzle half of the cooled salted caramel sauce over the batter and swirl gently with a knife. Repeat with the remaining batter and caramel, creating a second layer with swirls.
08 - Bake for 45 to 55 minutes, or until a toothpick or cake tester inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.
09 - Serve the cake warm or at room temperature. Drizzle with additional salted caramel sauce and garnish with sliced bananas or toasted chopped pecans if desired.