Sift flour, cornstarch, baking powder, and salt into a large bowl, then whisk it just a few times, set aside. In the bowl of an electric stand mixer, on medium speed, whip together butter, shortening, and sugar until very pale and fluffy, about 4 minutes, scraping down the sides of the bowl as needed.

Add in egg and mix until combined, then add egg white, vanilla, and almond extract and mix until combined. With mixer running, slowly add in dry ingredients and mix just until combined. Transfer dough to an airtight container and refrigerate 2 hours. Preheat oven to 375 during the last 10 minutes of refrigeration.

Scoop dough out a scant 1/4 cup at a time and roll into a ball. Place dough ball on a lightly floured surface, sprinkle top lightly with flour, then using something flat and smooth (such as the storage container lid), press and evenly flatten dough to 1/2 inch thick (about a 2 2/3 to 2 3/4 inch circular cookie).

Transfer flattened dough to a Silpat or buttered cookie sheet and repeat with remaining dough (using 2 cookie sheets). Bake at 375 for 9-11 minutes. Allow to cool 5 minutes on baking sheet before transferring to a wire rack to cool.

Cool completely then frost with Vanilla Frosting (note that frosting begins to set quickly, so sprinkle sprinkles immediately after frosting).