01 - Preheat the 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 golden brown and releases a nutty, fragrant aroma, approximately 5–7 minutes. 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. Set aside.
04 - In a large mixing bowl, combine the mashed bananas, granulated sugar, brown sugar, eggs, buttermilk, vanilla extract, and the slightly cooled browned butter. Stir until fully incorporated and smooth.
05 - Gradually fold the dry ingredient mixture into the wet ingredients using a spatula, mixing just until no dry pockets remain. Take care not to overmix, as this can produce a dense crumb.
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 of each layer emerges clean.
07 - Allow the cakes to cool in their pans for 10 minutes, then invert onto wire racks to cool completely before assembling.
08 - While the cakes bake, combine the granulated sugar and water in a medium saucepan over medium heat. Do not stir—simply swirl the pan gently. Once the mixture turns a deep amber color, remove from heat and carefully add the cubed butter, stirring 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 on medium speed until light and creamy, approximately 2 minutes. Gradually add the sifted powdered sugar and a pinch of salt, mixing on low until incorporated. Increase speed to medium and 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 a generous layer of caramel frosting over the top and drizzle with salted caramel sauce. Position the second layer on top. Apply frosting evenly over the top and sides of the entire cake. Finish with additional caramel drizzle and a sprinkling of flaked sea salt if desired.