Preheat oven to 325 F.
Sift the cake flour and ⅓ cup of sugar together 3 times.
In your electric stand mixer using the whisk attachment, whip egg whites, salt and cream of tarter on high speed until soft peaks form.
Turn the mixer down to medium speed and gradually add the 1 cup sugar and both extracts.
Turn back onto high speed and let it whip until the egg whites have glossy, stiff peaks.
Using a spatula or whisk, gradually fold in the sifted flour and sugar mixture in small batches. Be very gentle during this process to avoid deflating the egg whites. The key to a perfect angel food cake is maintaining as much air in the batter as possible.
Pour the batter into an ungreased 10-inch tube pan (angel food cake pan). The ungreased pan allows the batter to cling to the sides and rise properly. Smooth the top with a spatula. Bake in the preheated oven for 35-45 minutes, or until the cake is golden brown and springs back when lightly touched. Avoid opening the oven door during baking, as this can cause the cake to deflate.
Once baked, invert the warm cake immediately over a bottle or a funnel to cool completely. This helps prevent the cake from collapsing as it cools. Let the cake cool for at least 1-2 hours.
Run a thin knife around the edges of the cooled cake and center tube of the pan to loosen it. Invert the cool cake onto a serving plate.