Preheat the oven to 350 degrees. Butter, flour and line one 9-inch diameter x 2-inch deep cake pan or two 9-inch diameter x 1 1/2-inch deep pans with parchment paper. Bring a saucepan of water to a boil.
Using a wire whisk, stir the eggs in the bowl of a mixer fitted with the whip attachment. Whisk in the sugar.
Place the mixer bowl over the saucepan of boiling water. The water should be at least 2 inches bellow the bottom of the bowl. To prevent the eggs from cooking, use your hand whisk to stir the mixture continuously until it feels quite warm. The eggs should remain liquid and not become opaque or cooked. Failing to mix continuously will result in very sweet scrambled eggs!
When warm, immediately remove the bowl from the heat, place on the mixer and start whipping on high speed. Whip the eggs without stopping for 3 1/2 to 4 minutes.
While the eggs are whipping, melt the butter and pour it into a small bowl. Add the vanilla. Place the flour in the sifter and set aside.
The egg mixture is ready when the eggs have just cooled and at least tripled in volume. When you lift the whip out of the bowl, the batter should fall off the whip in ribbons.
Take the bowl off the mixer and sift a little less than 1/4 of the flour over the surface of the batter. Gently fold in the flour using the rubber spatula or your hand. You will hear the batter crunch if you are to rough. Repeat until all the flour is completely incorporated.
Pour a generous cup of the batter over the melted butter mixture in the small bowl. Thoroughly fold the batter into the butter. Slowly pour the butter mixture over the remaining batter in the mixer bowl in a circular motion. If you add the butter mixture too quickly the butter will sink, reducing the volume and toughening the cake. Gently fold together until none of the darker butter mixture is visible.
Carefully pour the batter into the prepared 9-inch diameter x 2-inch deep pan; it should be about 2/3 full. If using the two 9-inch diameter x 1 1/2-inch deep pans and making a 3 layer cake, pour 1/3 of the batter into one pan and the remaining 2/3 into the other. If making a 2 or 4 layer cake, divide the batter evenly between the two pans.
Set the cake pan(s) on a baking sheet and immediately place on the center rack in the oven. If using 9-inch diameter x 2-inch deep pan, bake for about 30 minutes and wait to open the oven until the cake has baked at least 25 minutes or it may fall. If using two pans, bake for about 20 minutes and wait to open the oven until the cake has baked at least 15 minutes.
The cake is done when it just starts to pull away from the sides of the pan. The cake will not spring back when gently pressed and a toothpick will not come out clean when it is ready.
After removing the cake from the oven, immediately run a metal icing spatula or knife around the inside of the pan(s) to loosen the cake. Let cool 5 minutes, then depan.
The cake may be stored, well wrapped, in the refrigerator for 1 day, or frozen for up to 1 week. Assemble as desired.