Preheat the oven to 350°F (177°C). Line three 9-inch round cake pans with parchment and spray the pans and parchment with nonstick spray.
In a large bowl or the stand mixer bowl fitted with the paddle, combine granulated sugar, brown sugar, flour, cocoa powder, baking soda, baking powder, and 1 1/4 teaspoons salt; mix on low until evenly combined and break up any clumps.
In a separate bowl whisk together the 3 large eggs, 2 egg yolks, sour cream, milk, vegetable oil, and 2 tablespoons vanilla until smooth.
Pour the wet ingredients into the dry ingredients and beat on low until just incorporated. Pour in the hot water and mix on low-medium until fully combined; the batter will be thin.
Divide the batter evenly among the prepared pans and bake for about 30 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Cool the cakes in their pans for 10 minutes, then invert onto a rack to cool completely before frosting.
To make the frosting, beat the very soft unsalted butter in a stand mixer fitted with the paddle on medium speed until smooth, about 3 minutes.
Turn the mixer off and sift in the confectioners' sugar and 3/4 cup cocoa powder. Mix on the lowest speed until the sugar and cocoa are incorporated, about 2 minutes, then increase to medium.
Add 1 teaspoon vanilla, 1/2 teaspoon salt, 3 tablespoons heavy cream, and 2 tablespoons salted caramel sauce; beat on medium for 3 minutes. Adjust thickness by adding more confectioners' sugar to thicken or 1 tablespoon additional cream at a time to thin.
Level the tops of the cakes with a serrated knife. Place one layer on a cake stand, spread a thin layer of frosting, then spoon 1/2 cup of the salted caramel sauce over the frosting.
Top with the second layer, repeat the thin frosting and 1/2 cup caramel, then place the final layer on top. Chill the assembled cake in the refrigerator for 1 hour to set.
Once set, finish frosting the top and sides of the cake with the remaining frosting, sprinkle with flaky sea salt, slice, and serve.