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 butter over medium heat. Cook, stirring, until foamy and brown flecks appear with a nutty aroma. Remove from heat and cool slightly.
03 - In a medium bowl, whisk together flour, baking soda, baking powder, and salt.
04 - In a large bowl, mix cooled brown butter, granulated sugar, and brown sugar. Beat in eggs one at a time. Stir in mashed bananas and vanilla extract.
05 - Fold dry ingredients into the wet mixture until just combined. Add sour cream and mix gently.
06 - Transfer batter to prepared pan. Smooth the top. Bake for 40 to 45 minutes, or until a toothpick inserted in the center emerges clean. Cool completely on a wire rack.
07 - Heat sugar in a dry saucepan over medium heat, stirring constantly, until melted and amber-colored. Whisk in butter until melted, then slowly add heavy cream while stirring. Mixture will bubble. Stir in sea salt. Let cool to room temperature.
08 - Beat softened butter until creamy. Gradually add powdered sugar and 1/2 cup cooled caramel sauce. Add milk as needed to achieve smooth, spreadable consistency.
09 - When cake is completely cool, top with caramel frosting or drizzle generously with salted caramel sauce. Garnish with additional sea salt flakes if desired.