Separate the egg whites and allow them to sit at room temperature for at least 30 minutes.
Preheat the oven to 350°F. In the bowl of a food processor or blender, process the gluten-free flour, cornstarch and powdered sugar together until smooth, about 30 seconds. Pour into a bowl and set aside.
Add the granulated sugar to the food processor or blender and pulse 5-7 times. You don’t want to turn it into powdered sugar, just a little finer than it is normally. Set aside.
In the bowl of a stand mixer fitted with the whisk attachment, or using a hand mixer, beat the egg whites on high speed until starting to foam, then add the salt and cream of tartar.
Add the vanilla extract and almond extract and continue whipping on high speed.
With the mixer running on high, slowly add the granulated sugar, 1 tablespoon at a time, until all the sugar is added and the mixture is glossy with soft peaks.
Using a rubber spatula, slowly fold in the flour mixture, ⅓ at a time. Do this carefully and slowly so you don’t deflate the egg whites. (This is the key to a good angel food cake.) Scoop into an ungreased 10-inch round pan.
Bake for 35-40 minutes, until lightly golden.
Remove the cake from the oven and immediately flip the cake upside down onto a wire rack. Cool the cake completely.
Once cooled, run a thin knife around the edge of the cake and gently tap the pan on the counter until the cake releases. Slice with a sharp serrated knife and serve.