I love this cake, and you can switch it up a thousand different ways - adding fruit, exploring flours, changing spices or nuts, etc. I outline a bunch of ideas up above!
Whisk the flours, salt, and nutmeg in a medium bowl and set aside.
Combine the eggs and 1 1/3 cup sugar in the bowl of a stand mixer. Using the whisk attachment beat until the mixture nearly triples in volume, until it becomes billowy and frosting-like. This can take a while - 5-7 minutes. By hand, using a spatula, immediately fold in the flour mixture. Add the melted butter, fold and stir until the batter is uniform.