Preheat your oven to 350°F (175°C). Do not grease the angel food cake pan, as the batter needs to cling to the sides for proper rising.
In a large mixing bowl, combine the egg whites, cream of tartar, and fine sea salt. Using your stand mixer or hand mixer, beat the egg whites on medium speed until they form soft peaks.
While the mixer is running, gradually add the granulated sugar, one tablespoon at a time. Continue beating until the mixture forms stiff, glossy peaks.
In a separate bowl, sift together the cake flour and a little bit of the remaining granulated sugar (about ¼ cup). Gently fold this mixture into the whipped egg whites using a rubber spatula.
Once the flour is fully incorporated, gently fold in the vanilla extract.
Transfer the batter into the ungreased angel food cake pan. Use a spatula to smooth the top and create an even surface.
Bake in the preheated oven for 35-40 minutes, or until the cake is golden brown and springs back when lightly pressed.
Once baked, remove the cake from the oven and immediately invert the pan onto a cooling rack.
After the cake has cooled completely, run a knife around the edges of the pan to loosen it. Carefully turn the cake out onto a serving plate.