For the Cake:

1. Preheat oven to 350°F. Lightly spray three 8-inch cake pans with nonstick cooking spray. Line the bottom of the pans with parchment paper, and lightly spray again.
2. In a stand mixer fitted with a paddle attachment, beat the butter at medium-high speed until softened and lightly whipped. Add the salt and sugar. Beat at medium-high speed until well combined.
3. With the mixer running on low speed, add one egg at a time. Increase the speed to medium-high and beat until fully incorporated. Repeat with the other two eggs.
4. Sift together the flour and baking powder in a separate bowl. Measure out the milk in a separate measuring pitcher. Measure the vanilla and stir into the milk. On low speed, add the dry ingredients and liquid mixture alternately to the butter mixture, starting and ending with the dry ingredients. Scrape the bottom and sides of the bowl after each addition, beating well until a uniform batter develops.
5. Divide the batter equally between the prepared pans. Bake for 25-30 minutes, or until the cake has a light spring when touched and a toothpick inserted in the center comes out clean.
6. Cool in the pans for 30 minutes. Turn cake out of the pans onto a cooling rack, remove the parchment paper, turn right side up, and allow to cool completely before decorating.

For the Caramel Sauce:

1. In a large clean pot, combine the sugar and corn syrup. Add 1/8 cup warm water and stir to begin dissolving the sugar.
2. Cook the mixture over high heat until it bubbles and turns light brown. Do not stir.
3. Once the sugar mixture is brown, turn off the heat and whisk vigorously while slowly pouring in the cream. It will bubble up significantly. Add the butter and whisk until melted.
4. Let the caramel cool to room temperature before adding to the buttercream.

For the Buttercream:

1. In the bowl of a stand mixer fitted with a paddle attachment, mix the softened butter on medium speed until it is smooth with no lumps.
2. Sift the confectioners’ sugar in a separate bowl. Add one cup at a time to the butter, beating very well after each addition.
3. Add the salt, vanilla, and heavy cream. Mix on medium-high speed until very light and fluffy, approximately 5 minutes.
4. Add 1/2 cup of the cooled prepared caramel to the buttercream. Mix until completely incorporated.

To Decorate:

1. Assemble and frost the cake rounds with the caramel buttercream, making a three-layer cake.
2. Refrigerate the decorated cake for 1 hour to set the frosting.
3. If necessary, reheat the remaining caramel briefly to get the right drizzling consistency. Once frosting on the cake has cooled and set, use pour or drizzle the remaining caramel over the top and the sides of the cake.
4. Let set for 10 minutes. Serve immediately, or store in the refrigerator until ready to serve.