1. Preheat the oven to 325 degrees. Lightly butter and flour two 9-inch round baking pans; set aside. In a medium bowl, whisk together flour, baking powder, and salt; set aside.

2. In the bowl of an electric mixer fitted with the whisk attachment, combine eggs and sugar. Beat until very thick and the batter falls from the whisk in a thick ribbon, 4 to 5 minutes. Beat in vanilla.

3. Meanwhile, heat milk and butter until simmering in a small saucepan. Add to the egg mixture in a slow, steady stream as you continue beating until combined. Gradually add dry ingredients and beat on low speed until just combined (or remove the bowl from the mixer and fold in dry ingredients until just combined). Pour the batter into the prepared pans. Bake until golden brown and starting to pull away from the sides of the pans, 55 to 60 minutes.

4. Remove from oven and cool on a wire rack for 15 minutes. Using an offset spatula or a knife, loosen cakes from pans. Invert onto a wire rack to cool completely. Re-invert one cake layer onto a serving plate; spread with 1 cup frosting. Top with remaining cake layer, spread frosting over the sides and top of cake to cover, and serve.