01 - Preheat 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. Swirl the pan frequently as the butter foams and subsides, watching carefully until the milk solids turn golden brown and release 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 tsp baking soda, and 1/2 tsp 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 tsp vanilla extract, and the cooled browned butter. Stir until well blended and smooth.
05 - Gradually add the dry ingredient mixture to the wet ingredients, folding gently with a spatula until just combined. Stop mixing as soon as no dry streaks remain to keep the crumb tender.
06 - Divide the batter evenly between the two prepared cake pans, smoothing the tops. Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean.
07 - Let the cakes cool in their pans for 10 minutes, then run a knife around the edges and 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—simply swirl the pan gently. Cook 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 (expect vigorous bubbling). Stir in 1 tsp flaked sea salt and let cool to room temperature.
09 - Beat 1/2 cup softened 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. Increase speed and beat in 4–5 tbsp of the prepared salted caramel sauce. Add 1–2 tbsp 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 cake with the remaining frosting. Finish with additional caramel drizzle and a sprinkle of flaked sea salt if desired.