Preheat the oven to 350°F and move the oven rack to the lowest position.
In a small bowl, mix the cornstarch and gluten-free flour and set aside.
In a large bowl, beat the egg whites and cream of tartar together on medium speed until foamy.
Gradually add the granulated sugar and powdered sugar on high speed, along with the vanilla and almond extracts and salt, until soft peaks form, and the meringue looks glossy.
Slowly sprinkle the cornstarch and flour mixture into the meringue, 1/4 cup at a time, and beat on medium speed until fully combined.
Pour the batter into an ungreased 10-inch x 4-inch angel food cake pan (tube pan). Smooth the top with a spatula. Cut through the batter in a circular motion with a butter knife.
Bake for 30-35 minutes or until golden brown and the top springs back when touched lightly.
Immediately turn the pan upside down onto a heatproof funnel or bottle and cool for 2 hours.
Once cooled, run a knife around the edges of the pan and invert the cake onto a platter. Slice with a serrated knife to avoid smashing.
Store leftovers in an airtight container.