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 3/4 cup unsalted butter in a light-colored saucepan over medium heat. Swirl the pan frequently as the butter foams and continue cooking until it turns golden brown and releases a nutty aroma. Immediately pour into a heatproof bowl and let cool slightly.
03 - In a medium bowl, whisk together 2 1/2 cups all-purpose flour, 1 teaspoon baking soda, and 1/2 teaspoon salt until evenly distributed.
04 - In a large bowl, combine the mashed bananas, 1 cup granulated sugar, 1/2 cup packed brown sugar, 2 eggs, 1/2 cup buttermilk, 2 teaspoons vanilla extract, and the cooled browned butter. Stir until well blended.
05 - Gradually fold the dry ingredient mixture into the wet ingredients using a spatula, mixing until just combined. Be careful not to overmix to keep the cake tender.
06 - Divide the batter evenly between the two prepared cake pans. Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes, then turn out onto wire racks to cool completely.
07 - While the cakes bake, combine 1 cup granulated sugar and 1/4 cup water in a medium saucepan. Heat over medium without stirring until the sugar turns a deep amber color. Remove from heat and carefully stir in 1/2 cup cubed butter until melted. Slowly whisk in 1/2 cup room-temperature heavy cream — expect vigorous bubbling. Stir in 1 teaspoon flaked sea salt and let the sauce cool to room temperature.
08 - Beat 1/2 cup softened unsalted butter with an electric mixer until light and creamy. Gradually add 2 cups sifted powdered sugar and a pinch of salt, beating on low until incorporated. Add 4–5 tablespoons of the prepared caramel sauce and 1–2 tablespoons milk or cream, then beat until the frosting is smooth and spreadable.
09 - 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. Place the second layer on top. Frost the top and sides of the cake with the remaining frosting. Drizzle additional caramel sauce over the surface and garnish with flaked sea salt if desired.