In a saucepan over medium heat, melt 2 cups of unsalted butter. Cook until golden brown, about 5-7 minutes, then remove and let cool slightly.

Preheat your oven to 350°F (175°C) and grease and flour two 9-inch round cake pans.

In a large mixing bowl, combine 2 1/4 cups of flour, baking powder, baking soda, and salt. Set aside.

In another large bowl, combine the browned butter with granulated sugar and brown sugar, beating until well mixed.

Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.

Alternate adding the dry ingredients and buttermilk to the wet mixture, mixing just until combined.

Divide the batter evenly between the prepared cake pans.

Bake for 25-30 minutes or until a toothpick comes out clean. Allow to cool in pans for 10 minutes.

Transfer to wire racks to cool completely.

In a saucepan over medium heat, melt 9 tablespoons of butter for the caramel. Stir in 3/4 cup brown sugar and cook for 1-2 minutes.

Slowly whisk in 1 cup heavy cream, bringing it to a gentle boil, then simmer for about 5 minutes until thickened.

Remove from heat and stir in 1 1/2 teaspoons vanilla extract and 1/4 tsp salt. Allow to cool.

Combine cold cream cheese and cooled brown butter in a mixing bowl, beating until creamy.

Gradually mix in powdered sugar until well combined and fluffy.

On a serving platter, place one layer of cake and spread a layer of caramel sauce. Top with the second layer and frost the cake with cream cheese frosting.

Drizzle any remaining caramel sauce on top and let it set before serving.