Preheat the oven to 350 degrees F. In a small saucepan, heat the milk and 1 tablespoon of butter, over medium heat. Put the eggs and 2 cups of sugar in a large mixing bowl, and with an electric mixer fitted with a wire whisk beat on medium-high speed until the mixture is pale yellow, thick, and has tripled in volume, about 8 minutes, using the mixer. With the machine on low, beat in the warm milk mixture. Sift the flour, baking powder, and salt together in another large mixing bowl. Add the egg mixture and vanilla, fold to mix thoroughly so the mixture is smooth. Grease 12 by 17-inch baking sheet pan with the remaining butter. Sprinkle with the remaining 2 tablespoons of sugar. Pour the cake batter evenly into the pan and bake until the cakes spring back when touched, about 15 minutes. Let cool for about 2 minutes. Sprinkle a piece of parchment paper with powdered sugar. Using a thin spatula or knife, loosen the edges of the cakes, then flip onto the paper. Cool completely.