After cutting out layers, save leftover vanilla sponge cake for crumbs, trifle, pudding, or tiramisu.
Heat oven to 350 degrees. Line two 11 1/2-by-17 1/2-inch jelly-roll pans with parchment paper. Sift together flour, cornstarch, baking powder, and salt.
Whip egg yolks and sugar on high speed until thick and pale. Reduce speed to low, and slowly add hot milk and vanilla extract. Beat at high speed until thick again. Transfer to a large bowl. Fold dry ingredients into yolk mixture in three additions.
Wash and dry mixing bowl and beater. Beat egg whites on low speed until frothy. Beat at high speed until soft peaks form.
Fold egg whites into batter in two additions. Divide between prepared pans; bake for about 15 minutes, or until cake is golden brown and springs back when pressed. Let cool completely in pans; cut out two 9-inch and two 6-inch circles.