Preheat oven to 350 degrees. Place flour and salt in a sieve set over a bowl; sift into bowl, and set aside. With a mixer, beat egg whites on medium-high until foamy, about 1 minute. Add cream of tartar; beat until soft peaks form. Continue to beat, gradually adding sugar; beat until stiff peaks form, about 2 minutes. Add vanilla; beat to combine.
Gently transfer egg-white mixture to a large, wide bowl. In four batches, using the sieve again, sift flour mixture over egg-white mixture. While turning the bowl, use a rubber spatula to fold in the mixture by cutting down the center and coming up the sides.
Gently spoon batter into an ungreased angel food cake pan with a removable bottom; smooth top. Cut a knife or small spatula through batter to release air bubbles. Bake until cake is golden and springs back when lightly pressed, 35 to 40 minutes. Invert pan; let cool in pan, 1 hour. Run a knife around the inside of the pan and around the tube to release cake, and unmold. Use knife to release cake from bottom of pan, and remove.⏱ 40 min