01 - Melt the butter in a saucepan over medium heat. Continue cooking, swirling the pan occasionally, until the butter foams and golden-brown bits form at the bottom, about 5–7 minutes. Pour into a bowl and let cool for 10 minutes.
02 - Preheat the oven to 350°F. Grease a 9-inch round cake pan or loaf pan and line with parchment paper.
03 - In a medium heavy-bottomed saucepan, heat the sugar over medium heat, stirring constantly until fully 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 smooth and well blended.
06 - Add the dry ingredient mixture to the wet ingredients, folding 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 over the batter and swirl gently with a knife. Repeat with the remaining batter and caramel, swirling again.
08 - Bake for 45–55 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
09 - Serve warm or at room temperature. Drizzle with additional salted caramel and garnish with sliced banana or toasted chopped pecans if desired.