Adjust an oven rack to the lower third position and preheat the oven to 350 degrees. Butter or coat with cooking spray a 9-inch layer cake pan. Line the bottom with a round of cooking parchment or waxed paper. Butter the paper or coat with cooking spray and dust the inside of the pan lightly with all-purpose flour. Knock out excess flour.
In a medium bowl, whisk the cake flour with the baking powder and salt and set aside.
Place the milk and butter in a small heavy saucepan and set overlow to medium heat. The milk and butter must get very hot while the eggs beat, and it's important the liquid is ready at about the same time as the eggs or the eggs may deflate.
Beat the eggs and yolks with an electric mixer on high speed for about 5 minutes until thickened and light in color. Reduce the speed to medium and add the sugar 1 tablespoon at a time, beating for 10 to 15 seconds after each addition. Once all the sugar has been added, increase the speed to high and beat for 5 minutes. Beat in the vanilla. On low speed, add the dry ingredients and beat only until incorporated. Scrape the bowl, handling the batter as gently as possible.
Quickly bring the milk and butter mixture to the boil. While beating on low speed, add the liquid in a steady stream to the batter, taking 15 to 20 seconds to do so. Don't dally. As soon as the batter is smooth scrape it into the prepared pan and place the pan in the oven.
Bake 25 to 30 minutes, until the top of the cake is a deep golden brown color, it springs back when gently pressed, and the cake just begins to pull away from the sides of the pan. Do not over-bake. Cool for 10 minutes on a wire rack. If the cake is sticking at any point to the side of the pan, release it with the tip of a small sharp knife. Cover the cake with a wire rack and invert. Remove the pan and paper liner. Cover the cake with another rack, and re-invert so that the cake cools right side up. The layer will be about 1 inch high.