01 - Preheat the oven to 350°F (175°C). Grease and flour two 8-inch (20 cm) 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, swirling frequently. Continue cooking until the butter turns golden brown and releases a nutty, toasted aroma, about 5 to 7 minutes. Transfer immediately to 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 1 1/2 cups 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 thoroughly incorporated.
05 - Gradually fold the dry ingredient mixture into the wet ingredients using a spatula, mixing just until no dry pockets remain. Avoid overmixing to keep the crumb tender.
06 - Divide the batter evenly between the two prepared pans, smoothing the tops. Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes, then invert 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, gently swirling the pan occasionally, until the mixture 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, taking caution as the mixture will bubble vigorously. Stir in 1 teaspoon flaked sea salt and let cool to room temperature.
08 - Beat 1/2 cup softened unsalted butter with an electric mixer until light and creamy, about 2 minutes. Gradually add 2 cups sifted powdered sugar and a pinch of salt, beating on low until combined. Increase speed and beat in 4 to 5 tablespoons of the prepared salted caramel sauce. Add 1 to 2 tablespoons milk or cream as needed to reach a smooth, spreadable consistency.
09 - Place one cooled 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 cake layer on top. Frost the top and sides of the assembled cake with the remaining frosting. Finish with additional caramel sauce drizzled over the top and a sprinkle of flaked sea salt.