Sift the confectioners’ sugar with the cake flour onto a sheet of wax or parchment paper. Repeat two more times.
Move the center oven rack down one notch and preheat the oven to 325°F.
To separate the egg whites from their yolks, crack the eggs one at a time into a small bowl. Lift out the yolk and place it in a separate container with a little water in it (see Tip), and pour the whites, one at a time, into a 2-cup measuring cup. You need a total of 1½ cups of totally yolk-free egg whites.
Pour the egg whites into the bowl of a stand mixer fitted with a whisk attachment or a mixing bowl and use a handheld mixer. Beat on medium-low speed until frothy, then sprinkle in the cream of tartar. Beat on medium-high speed until glossy, soft peaks form.
Sift or gradually spoon small amounts of the granulated sugar into the egg whites, beating at medium-high speed as you go and maintaining the beaten peaks. Add the salt and vanilla, beating to incorporate. Remove the bowl from the mixer.
In three additions, use a flexible spatula to fold in the sifted confectioners’ sugar–cake flour mixture to create a soft batter. Do not overmix. Transfer to your tube pan, spreading the batter gently and evenly. Bake on the repositioned rack for 40–45 minutes, until the surface is lightly browned, with some wide cracks. Invert the cake, still in its pan, on a wire rack or with its center tube set on the long neck of a sturdy bottle to cool. Once it’s completely cooled (at least 1 hour), run a thin knife around the cake’s edges to dislodge it.
Tip: Leftover yolks from this recipe can be refrigerated with a little water in an airtight container for up to 2 days. Use them to make mayonnaise, hollandaise sauce, lemon curd, ice cream, crème brûlée, and more.