01 - Preheat oven to 350°F (175°C). Grease and flour two 8-inch round cake pans, then line the bottoms with parchment paper.
02 - Melt the unsalted butter in a light-colored saucepan over medium heat, swirling frequently. Continue cooking until the butter turns a deep golden brown and releases a fragrant, nutty aroma. Transfer immediately to a heatproof bowl and let cool slightly.
03 - In a medium bowl, whisk together the all-purpose flour, baking soda, and salt until evenly distributed.
04 - In a large mixing bowl, combine the mashed bananas, granulated sugar, brown sugar, eggs, buttermilk, vanilla extract, and cooled brown butter. Stir until thoroughly blended and smooth.
05 - Gradually fold the dry ingredient mixture into the wet ingredients, mixing gently until just combined. Avoid overmixing to keep the cake tender.
06 - Divide the batter evenly between the two prepared cake pans, smoothing the tops. Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean.
07 - Allow the cakes to cool in their pans for 10 minutes, then turn them out onto wire racks to cool completely before assembling.
08 - While the cakes bake, combine granulated sugar and water in a medium saucepan over medium heat. Do not stir—allow the mixture to cook undisturbed until it turns a deep amber color. Remove from heat and carefully stir in the cubed butter until fully melted. Slowly whisk in the room-temperature heavy cream, expecting vigorous bubbling. Stir in the flaked sea salt and let the sauce cool to room temperature.
09 - Beat the softened butter with an electric mixer until light and creamy. Gradually add the sifted powdered sugar and a pinch of salt, mixing on low speed until incorporated. Beat in 4–5 tablespoons of the prepared salted caramel sauce. Add milk or cream 1 tablespoon at a time until the frosting reaches a smooth, spreadable consistency.
10 - Place the first cake layer on a serving plate. Spread an even layer of caramel frosting over the top and drizzle with salted caramel sauce. Position the second layer on top. Frost the top and sides of the entire cake with the remaining frosting. Finish with an additional drizzle of caramel sauce and a sprinkle of flaked sea salt if desired.