Preheat the oven to 350 degrees F. In a small saucepan, heat the milk and 2 tablespoons butter together. Using an electric mixer fitted with a wire whip, combine the eggs and 2 cups sugar together. Beat on medium-high speed for about 8 minutes, or until the mixture is pale yellow, thick and has tripled in volume. With the machine running slowly add the heated milk. In a mixing bowl sift the flour, cocoa powder, baking powder, and salt together. Fold the flour mixture into the egg mixture and mix thoroughly so that there are no lumps and the mixture is smooth. Fold in the vanilla. Grease a 1/2 sheet pan with 2 teaspoons of butter. Sprinkle with 2 tablespoons of sugar. Pour the cake batter evenly into the pan and bake for about 25 minutes, or until the cake springs back when touched. Cool for about 2 minutes. Using a thin knife, loosen the edges of the cake, then flip onto a wire rack and cool completely.