Position oven rack to the lower third position. Preheat oven to 325°F (163°C).
Sift the cake flour and powdered sugar together three times. Set aside.
In the bowl of a stand mixer fitted with the whisk attachment, or in a large mixing bowl using an electric mixer, add the egg whites and beat on low-medium speed until foamy.
Add the cream of tartar and salt then increase the speed to medium-high.
Gradually add the granulated sugar, about one tablespoon at a time, and continue beating the egg whites until stiff glossy peaks form. Add the vanilla extract and mix on low speed until just combined.
Sift about one-fourth of the dry ingredients over the beaten egg whites and gently fold it in. Repeat, folding in the dry ingredients one-fourth at a time.
Scoop the batter into an ungreased 10-inch angel food cake pan or tube pan. Cut a knife through the batter to remove any air pockets, then smooth it out into one even layer.
Bake the cake at 325°F (163°C) for 40-45 minutes or until the top is lightly golden brown and a toothpick inserted into the cake comes out clean.
Remove the cake from the oven and invert the cake pan onto a wire rack to cool completely. Once cooled, use a knife to loosen the sides of the cake from the pan and carefully remove it. Slice into pieces, serve, and enjoy!