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 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, approximately 5 to 7 minutes. Immediately transfer 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 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 browned butter. Stir until thoroughly incorporated.
05 - Gradually fold the dry ingredient mixture into the wet ingredients, stirring gently until just combined. Take care not to overmix, as this will yield a denser crumb.
06 - Divide the batter evenly between the two prepared cake pans, smoothing the tops with a spatula. Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
07 - Allow the cakes to rest in their pans for 10 minutes, then invert onto wire racks to cool completely before assembling.
08 - In a medium saucepan, combine 1 cup granulated sugar and 1/4 cup water. Heat over medium heat without stirring until the sugar dissolves and turns a deep amber color. Remove from heat and carefully add 1/2 cup cubed butter, stirring 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.
09 - 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, mixing on low speed. Once incorporated, beat in 4 to 5 tablespoons of the prepared salted caramel sauce. Add 1 to 2 tablespoons milk or cream as needed 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 cake layer on top. Frost the top and sides of the entire cake, then finish with additional caramel drizzle and a sprinkling of flaked sea salt if desired.