While the egg whites are coming to room temperature, in a large bowl, sift flour (either cake flour or all purpose flour + cornstarch) and powdered sugar together, 5 times.* Set aside.
With a hand mixer or standing mixer on medium speed, whip egg whites, vanilla extract, almond extract (if using), salt and cream of tartar until soft peaks form.
Immediately invert the pan upside-down, allowing it to cool for about 1 hour. (I inverted mine and rested it on a heat proof bottle.) Once cooled, use a knife to loosen the sides of the cake and invert cake onto a plate/serving dish (it might take a couple gentle shakes and taps to get the cake to come out of the pan).
*While this might seem like overkill, sifting the ingredients is imperative to making sure the angel food cake is light and airy. In my testing, I found that sifting the ingredients together 5 times yielded the lightest cake.
**Adapted from Taste of Home.