Note: This recipe has been adapted from "Desserts by Pierre Herme," by Dorie Greenspan. Copyright 1998 by SOCREPA and Dorie Greenspan. Reprinted by permission of SOCREPA. Published by Little, Brown.
Center a rack in the oven and heat the oven to 350 degrees. Butter a 9-inch pan, dust the interior with flour, and tap out the excess. Set aside.
Pour a few inches of water into a skillet large enough to hold the bowl of your electric mixer. Bring the water to a gentle simmer. Melt the butter, and set it aside to cool -- it should be just warm when you're ready for it.
Hand-whisk the eggs and sugar together in the mixer bowl. Place the bowl in the skillet of simmering water and, whisking steadily, heat the mixture about 4 minutes, until it is foamy, slightly pale, and reads between 130 and 140 degrees on an instant-read thermometer. Remove the bowl from the water. Fit the electric mixer with a whisk attachment, and beat the mixture on high speed until it cools to room temperature and triples in volume, about 5 to 8 minutes. You'll know it's just right if, when you lift the whisk, the batter falls back into the bowl and forms a ribbon that remains on the surface for 10 seconds before it dissolves.
Stir about 2 tablespoons of batter into the slightly cooled butter, and set it aside. With a large flexible rubber spatula, gently fold the flour into the batter in two or three additions (you might find it most convenient to add the flour to the bowl by shaking it through a strainer), taking care to handle the batter gently in order to maintain its bubble structure. The batter will lose volume as you fold in the flour and later the butter. This reaction is inevitable and shouldn't jeopardize the success of the finished cake. Still working with the spatula, fold in the butter mixture. At this point, the batter must be used immediately.
Pour the batter into the prepared 9-inch pan, and bake for 28 to 33 minutes, or until the top is golden and springy to the touch and a toothpick inserted in the center of the cakes comes out clean. Transfer the cake to a cooling rack; unmold after 5 minutes. Turn the cake right-side-up to cool to room temperature on the rack.