SpinningSugar:Yes. As the directions state:

In a medium bowl or large measuring cup, whisk the 6 eggs [that would be whole eggs--whites and yolks] well until the whites are completely blended [no strands of clear white; the mass will be smooth, not clumpy, and lemon-colored], then add the 6 egg yolks and whisk more until the eggs are smooth. [Again, the blend will be smooth as silk, not clumpy when picked up and spilled with a spoon, and now darker than before with the addition of the extra 6 yolks.]

SpinningSugar: I’m surprised the butter didn’t melt completely after two hours of beating! I don’t believe you are doing anything wrong at all. Just add the sugar very slowly, as written, and do so in batches. Don’t expect the entirety of sugar to dissolve into the butter, as the more you add, the less will dissolve into the butter. Take a close look at the butter-sugar a few seconds after you begin the incorporate the sugar. Feel how “grainy” the sugar is right now? Now beat for about five minutes and take another look. You will see the grains are much, much smaller (though not completely gone) and the butter is fluffy and light. This is the consistency you are seeking. Continue to add the balance of the sugar in batches and don’t worry. The remainder of the sugar granules will dissolve during cooking, but the light, fluffy consistency of the butter-sugar suspension — only possibly through slowly incorporating — is critical to achieving your goal.

SpinningSugar: I use Swans Down cake flour because of its easy availability, but there are others. King Arthur Flour (I love them!) makes an excellent cake flour named “Queen Guinevere” (my personal favorite), and Pillsbury makes “Softasilk” that I have also used with equal success. Definitely never use any cake flour that is “self-rising”.