01 - Preheat oven to 350°F. Grease and flour two 8-inch round cake pans, tapping out any excess flour.
02 - Melt 3/4 cup unsalted butter in a light-colored saucepan over medium heat. Swirl the pan frequently as the butter foams and subsides. Continue cooking until the milk solids turn golden brown and release a fragrant, nutty aroma, about 3 to 5 minutes. Immediately transfer 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 fully incorporated and the mixture is smooth.
05 - Gradually fold the dry ingredient mixture into the wet ingredients using a spatula, mixing only until no visible streaks of flour remain. Avoid overmixing to keep the cake tender.
06 - Divide the batter evenly between the two prepared cake pans, smoothing the tops. Bake on the center rack for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
07 - Let the cakes cool in their pans for 10 minutes, then invert onto wire racks to cool completely before frosting.
08 - While the cakes bake, combine 1 cup granulated sugar and 1/4 cup water in a medium saucepan over medium heat. Do not stir — swirl the pan gently to dissolve the sugar evenly. Cook until 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, taking caution as the mixture will bubble vigorously. Stir in the flaked sea salt and let cool to room temperature.
09 - Using a hand mixer or stand mixer, beat the softened butter on medium speed until pale and creamy. Gradually add the sifted powdered sugar and a pinch of salt, mixing on low until incorporated. Increase speed and beat in 4 to 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.