Put the egg whites in the bowl of a stand mixer and bring them to room temperature.
Sift together the cake flour, cocoa powder and ¾ cup (150 grams) of the sugar. After sifting, stir well and make double-sure everything is well mixed. Set aside.
Add the cream of tartar to the egg whites and beat with the whisk attachment until frothy. Continue beating, increasing speed gradually, until the egg whites are soft, but not quite stiff. Continue beating, gradually adding the remaining sugar one tablespoon at a time, until the egg whites are thick and billowy. Beat in the salt and vanilla.
With mixer on lowest speed, gradually add the sifted flour mixture. When flour mixture is fully blended, remove from the stand and with a heavy duty scraper, fold in any unevenly mixed cocoa mixture.
Scrape the cake batter into the angel food cake pan. It should come a little over half way up the sides.
Bake at 350 for 35 to 40 minutes. Remove from the oven and turn upside down on the pan’s legs. Allow the cake to cool for about an hour, then carefully slide a knife between the edges of the pan and the cake and push the cake out. Slide the knife between the cake and the pan bottom to loosen.
Let the cake cool completely.
Notes
If using extra large eggs, you'll most likely only need 12.