1. Preheat the oven to 350°F (175°C). Ensure the oven rack is positioned in the lower third of the oven.
2. In a bowl, sift together the cake flour and 3/4 cup of granulated sugar. Set aside.
3. In a large bowl or the bowl of a stand mixer fitted with a whisk attachment, beat the egg whites on medium speed until frothy.
4. Add the cream of tartar and salt to the egg whites. Increase the speed to medium-high and continue beating until soft peaks form.
5. Gradually add the remaining 3/4 cup of granulated sugar to the egg whites, about 1-2 tablespoons at a time, while continuing to beat on medium-high speed. Beat until stiff, glossy peaks form. Be careful not to overbeat.
6. Add the vanilla extract (and almond extract, if using) to the egg white mixture and gently fold it in with a rubber spatula.
7. Sprinkle a small amount of the flour mixture over the egg whites and gently fold until just combined. Repeat this process with the remaining flour mixture, gently folding until no streaks of flour remain.
8. Pour the batter into an ungreased angel food cake pan. Gently smooth the top with a spatula.
9. Bake in the preheated oven for 35–40 minutes, or until the top is golden brown and the cake springs back when lightly touched.
10. Remove the cake from the oven and immediately invert the pan onto a cooling rack. Let the cake cool completely in the pan upside down. This helps prevent it from collapsing.
11. Once the cake is completely cooled, run a knife around the edges of the pan to loosen the cake. Gently remove the cake from the pan.

Serve slices of Angel Food Cake plain or with your favorite toppings, such as fresh fruits, whipped cream, or glaze.