Step 1Adjust a rack to the center of the oven and heat to 350 degrees. Butter or spray the pans, line the bottoms of the pans with parchment, and butter or spray again.
Step 2To make a double boiler, fill a saucepan with an inch or two of water and bring to a simmer over medium heat. Combine the eggs and sugar in a bowl that will fit over the saucepan with water (or use the bowl of your standing mixer). Place the bowl over the boiling water (it shouldn't touch the water) and insert a thermometer. Whisk continuously until the temperature reaches 110 degrees, about 3 to 4 minutes.
Step 3Remove the bowl from the heat (transfer to the bowl of a mixer if you haven't used it) and whip on high speed until the eggs triple in volume, about 5 minutes. On low speed, stream in the melted butter and mix only until combined.
Step 4Add the sifted flour to the mixture in three batches, mixing with a whisk (or the whisk attachment of your mixer) each time until just combined. Try not to deflate the batter; mix as little as possible.
Step 5Pour the batter into the two pans, smoothing over the tops. Bake for 15 minutes. Rotate pans and bake 10 minutes more. The cake is done when it springs back when touched lightly and begins to pull away slightly from the edges of the pan.
Step 6Cool the cakes in the pans on a rack for 15 minutes. Invert the pans over a rack, remove the pans, then invert again. Keep at room temperature (or freeze) until ready to assemble. For a two-layer cake, level the layers and frost. For a four-layer cake, level the layers, cut each in half horizontally, and frost.