01 - Preheat oven to 350°F (175°C). 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. Cook, stirring, until foaming subsides and golden brown flecks develop. Remove from heat and allow to cool slightly.
03 - In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt.
04 - In a large bowl, mix the cooled brown butter with granulated sugar and packed light brown sugar. Mix in eggs one at a time, beating well after each addition. Stir in mashed bananas and vanilla extract.
05 - Fold the dry mixture into the wet mixture using a spatula. Add sour cream and mix gently until just combined. Do not overmix.
06 - Pour batter into prepared cake pan and smooth the surface. Bake for 40 to 45 minutes or until a toothpick inserted in the center emerges clean. Cool completely on a wire rack.
07 - For the caramel, heat 1 cup granulated sugar in a dry saucepan over medium heat, stirring constantly, until melted and amber in color. Carefully whisk in cubed unsalted butter until fully melted. Gradually add heavy cream; mixture will bubble. Stir in flaky sea salt. Cool to room temperature.
08 - For the frosting, beat 1/2 cup softened unsalted butter until creamy. Gradually add powdered sugar and 1/2 cup cooled salted caramel sauce. Add milk, a tablespoon at a time, until desired consistency is reached.
09 - Once cake is completely cool, cover with caramel frosting or drizzle generously with salted caramel sauce. Optionally, decorate with additional sea salt flakes.