01 - Preheat oven to 350°F. 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, until it turns a deep golden brown and releases a nutty, fragrant aroma. Transfer to a heatproof bowl and let cool for 10-15 minutes.
03 - In a medium bowl, whisk together the all-purpose flour, baking soda, and salt until evenly distributed.
04 - In a large bowl, combine the mashed bananas, granulated sugar, brown sugar, eggs, buttermilk, vanilla extract, and cooled brown butter. Stir vigorously until the mixture is smooth and fully incorporated.
05 - Gradually fold the dry ingredient mixture into the wet ingredients using a spatula, mixing until just combined. Avoid overmixing to keep the crumb tender.
06 - Divide the batter evenly between the two prepared cake pans, smoothing the tops with a spatula.
07 - Bake for 35-40 minutes, or until a toothpick inserted into the center of each layer comes out clean. Let the cakes rest in their pans for 10 minutes, then turn out onto wire racks to cool completely.
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 — allow the sugar to dissolve and cook until it reaches a deep amber color. Remove from heat and carefully whisk in the cubed butter until melted, then slowly pour in the room-temperature heavy cream, whisking constantly to prevent splattering. Stir in the flaked sea salt and let the sauce cool to room temperature.
09 - Beat 1/2 cup softened butter with an electric mixer until light and creamy. Gradually add the sifted powdered sugar and a pinch of salt, beating on low until combined. Mix in 4-5 tablespoons of the prepared salted caramel sauce. Add 1-2 tablespoons of milk or cream as needed until the frosting reaches a smooth, spreadable consistency.
10 - Place one cooled 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. Frost the top and sides of the entire cake, then finish with additional caramel drizzle and a sprinkle of flaked sea salt if desired.