Preheat your oven to 350°F (175°C). In a food processor, spin the granulated sugar for about 2 minutes until it becomes superfine. Sift half of this superfine sugar together with the salt and the sifted cake flour; set the remaining half of the sugar aside. This helps prevent lumps and ensures your cake comes out light and airy.
In the bowl of a stand mixer fitted with the whisk attachment, combine the room-temperature egg whites, warm water, vanilla extract, almond extract (if using), and cream of tartar. Mix on low speed for about 1 minute, allowing everything to blend gently before building volume.
Gradually sift in the reserved superfine sugar, beating continuously at medium speed. Keep beating until medium peaks form – the meringue should hold its shape but not be stiff. I find adding the sugar slowly helps create a smooth, stable foam.
Sift a portion of the flour, salt, and sugar mixture from Step 1 over the meringue to dust the top. Gently fold it in using a spatula, being careful not to deflate the foam. Repeat this process in several additions until all the flour mixture is incorporated and you have a smooth, airy batter.
Carefully spoon the batter into an ungreased tube pan, smoothing the top. Bake at 350°F (175°C) for 35 minutes. Check for doneness by inserting a wooden skewer halfway between the inner and outer walls; it should come out dry when the cake is done.
Once baked, cool the cake upside down on a cooling rack for at least an hour before removing it from the pan. This helps prevent it from collapsing and ensures the iconic fluffy texture of angel food cake. I find the cake is much easier to handle (and tastes even better) when completely cooled.