1. Warm the bowl of an electric mixer. Beat the eggs with the sugar and vanilla at the highest speed until the mixture stands in stiff peaks when the beater is withdrawn. Depending on the power of the mixer, this should take from five to thirty minutes. It is important not to underbeat the mixture. Scrape the sides of the bowl with a rubber spatula from time to time so the ingredients will be well blended.
2. Meanwhile, grease two nine-inch or three eight-inch cake pans that are one and one-half inches deep. Line the pans with waxed paper and grease the paper. Melt the butter and cool to lukewarm. Set heat control at moderate (350° F.) and place rack in the lower third of the oven.
3. Divide the flour into six to eight portions and sift over the egg mixture a portion at a time. Use a rubber spatula to fold the flour in gently after each addition.
4. Add the butter, about a teaspoon at a time, and fold it in gently but completely.
5. Turn the batter into the prepared pans and bake thirty-five to forty minutes. When done, the cake will rebound to the touch when pressed gently in the center.
6. Turn the cakes out onto a cooling rack, remove the paper and let cool. Frost with desired frosting and genoise praline powder