Preheat the oven to 350 degrees F.
Combine the warm melted butter and vanilla extract; set aside.
Sift the flour together with 3 tablespoons of the sugar.
Combine the eggs and the remaining sugar in a mixing bowl, and set over a large bowl of very hot water.
Mix with your hand until warm to the touch, then remove from the heat and whip on high speed until very fluffy, and batter falls from the beater in long, thick ribbons.
Fold the flour mixture carefully into the egg mixture, in three additions.
Mix a little of the batter into the melted butter, and then pour back into the mixing bowl and fold until combined, taking care not to deflate the air from the batter.
Bake in an ungreased 8- or 9-inch round cake pan for 30 minutes, or until a toothpick inserted in the thickest part of the cake comes out clean.
Cool completely and cut horizontally into two layers.