Place egg whites in a large, deep bowl. Cover with a clean cloth. Allow egg whites to warm to room temperature, about 30 to 60 minutes.
Preheat oven to 250 degrees. Line a baking sheet with parchment paper or plain brown paper.
Beat egg whites and cream of tartar with an electric mixer until frothy. Gradually add granulated sugar, 1 tablespoon at a time, beating constantly. Sift together powdered sugar and cornstarch. Add to egg white mixture, 1 tablespoon at a time, beating constantly. Beat until stiff peaks form. Beat in almond extract or vanilla.
Spoon into pastry bag fitted with a large star tip. Pipe egg whites onto baking sheet. Bake for 2 hours. Turn off oven and let cool in closed oven for 3 to 4 hours. Remove from parchment paper with spatula and store in an air tight container.