Preheat the oven to 350 degrees and adjust oven racks if necessary for the angel food cake to be right in the center of the oven.
Be sure that all kitchen equipment you will be using is completely free of any grease. Even though already clean, I usually give mine an extra hand scrub to be sure there is not any grease, as even the tiniest bit will ruin an angel food cake.
Sift the flour and powdered sugar together 3 times. Set aside.
Pour the egg whites, cream of tartar, vanilla, almond extract, and salt into a mixing bowl.
Begin to beat at a high speed.
Once the egg whites start to foam up, add the sugar in a slow and steady stream with the beaters still running.
Continue to beat on high until stiff peaks form.
FOLD, not stir the flour/powdered sugar into the egg whites a ¼ cup at a time.
Once the previous ¼ cup has been folded in halfway, add the next ¼ cup. Repeat until all the flour/powdered sugar has been added and is completely folded in.
Gently spoon the batter into an UNGREASED 10-inch tube pan.
Run a sharp knife in a clockwise (or counterclockwise) circle around the tube pan to even out the batter and pop large air bubbles, but do not deflate the batter.
Bake at 350 degrees in the center of the oven for 40 minutes.
IMMEDIATELY, invert the hot angel food cake and set the tube pan upside down on a wire rack to cool after removing it from the oven.
Do not remove the outside piece of the tube yet. Allow the angel food cake to cool completely while upside down.
Once cool, flip back over and run a sharp knife around the outside edge and inside the tube. Remove the outside piece of the pan if using a 2-piece tube pan, and then remove the cake from the inside piece.
If using a 1-piece tube pan, turn the pan over at a slight angle and use a thin spatula to loosen the bottom just a bit. The angel food cake should pop right out.
Slice with a serrated knife and serve with fresh fruit and whipped cream.