Preheat your oven to 350°F (175°C). Cut out three 9-inch parchment paper rounds to fit the bottoms of your cake pans. Generously spray the sides and bottoms of each pan with nonstick cooking spray, place a parchment round in the bottom of each, then spray again. It’s crucial to coat both the pans and paper thoroughly to prevent the cakes from sticking. Set the prepared pans aside.

In the bowl of a stand mixer fitted with the paddle attachment—or using a handheld electric mixer and a large mixing bowl—combine the granulated sugar, brown sugar, flour, cocoa powder, baking soda, baking powder, and salt. Mix on low speed until all dry ingredients are fully combined, breaking up any large clumps with your hands if necessary.

In a separate bowl, whisk together the eggs, egg yolks, sour cream, milk, oil, and vanilla extract until the mixture is smooth and fully blended. Pour the wet ingredients into the dry mixture and beat on low speed just until everything is incorporated. Slowly pour in the hot water and continue mixing until fully combined; this should take about 1 minute. Note that the batter will be quite thin.

Evenly divide the batter between the three prepared pans. Bake in the preheated oven for about 30 minutes, or until a toothpick or cake tester inserted in the center comes out clean or with only a few moist crumbs. Allow the cakes to cool in their pans for 10 minutes, then carefully remove them from the pans and transfer them to a wire rack to cool completely before applying the frosting.

In the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter on medium speed until completely smooth and creamy, about 3 minutes. Turn off the mixer and sift the confectioners’ sugar and cocoa powder directly into the bowl. Turn the mixer to the lowest speed and blend until the sugar and cocoa are absorbed by the butter, which should take about 2 minutes. Increase the speed to medium, then add in the vanilla extract, salt, heavy cream, and salted caramel sauce. Beat the frosting mixture for about 3 minutes, until light and fluffy. If the frosting is too thin, add a bit more powdered sugar; if it's too thick, gradually mix in additional heavy cream, 1 tablespoon at a time, until you reach your desired consistency.

With a serrated knife, carefully level the tops of each cake layer to create even, flat surfaces. Place the first cake layer on a large plate or cake stand. Spread a thin layer of frosting on top, followed by about 1/2 cup of salted caramel sauce. Add the second cake layer and repeat the process—spreading a thin layer of frosting and another 1/2 cup of caramel. Place the final cake layer on top, then refrigerate the stacked cake for 1 hour to allow it to set. Once chilled, finish frosting the top and sides of the cake with the remaining chocolate frosting. Sprinkle the top with flaky sea salt. Slice and serve, or store the cake in the refrigerator for up to 5 days.