01 - Preheat oven to 350°F. Grease and line a 9-inch round cake pan with parchment paper.
02 - In a small saucepan, melt 1 cup unsalted butter over medium heat, stirring until the butter foams and develops brown flecks with a nutty aroma. Remove from heat and let cool slightly.
03 - In a medium bowl, whisk together all-purpose flour, baking soda, baking powder, and salt.
04 - In a large bowl, combine the cooled brown butter, granulated sugar, and brown sugar. Beat in eggs one at a time. Stir in mashed bananas and vanilla extract.
05 - Fold the dry mixture into the wet ingredients. Add sour cream and mix gently until just combined.
06 - Transfer batter to the prepared pan. Smooth the surface and bake for 40 to 45 minutes or until a toothpick inserted in the center comes out clean. Cool completely on a wire rack.
07 - In a clean saucepan over medium heat, cook granulated sugar, stirring constantly, until melted and amber. Carefully whisk in cubed unsalted butter until smooth. Slowly add heavy cream; the mixture will bubble. Stir in flaky sea salt and cool to room temperature.
08 - In a bowl, beat softened unsalted butter until creamy. Gradually incorporate powdered sugar and 1/2 cup salted caramel sauce. Add milk, one tablespoon at a time, until the frosting reaches desired consistency.
09 - Once the cake is cooled, cover with caramel frosting or drizzle generously with salted caramel sauce. Sprinkle additional sea salt flakes if desired.