For the Caramel Sauce:
12 tablespoons (1 1/2 sticks) unsalted butter
1 1/2 cups firmly packed dark brown sugar
3/4 cup firmly packed light brown sugar
3/4 cup whole milk
1/4 teaspoon salt

For the Caramel Cupcakes:
1 3/4 cups unbleached all-purpose flour
1 1/2 teaspoons baking powder
3/4 teaspoon salt
12 tablespoons (1 1/2 sticks) unsalted butter, softened
1 1/2 cups sugar
3 large eggs, broken into a small bowl
1 teaspoon pure vanilla extract
3/4 cup whole milk

For the Salted Caramel Buttercream:
3/4 cup reserved caramel sauce
2 cups confectioners’ sugar, sifted through a strainer
2 tablespoons unsalted butter, softened
2 tablespoons egg substitute, such as Egg Beaters
1/4 teaspoon salt

Topping:
Coarse-grain salt