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

Add egg and mix until combined. Then add egg white, vanilla, and almond extract and mix until combined. With the mixer running, slowly add the dry ingredients and mix just until combined. Transfer dough to an airtight container and refrigerate for 2 hours. Preheat oven to 375°F 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 a container lid), press and evenly flatten dough to 1/2" thick (this should result in about a 2 2/3" - 2 3/4" circular cookie).

Transfer flattened dough to a Silpat or buttered cookie sheet and repeat with remaining dough (you'll need 2 cookie sheets). Bake in preheated oven for 9-11 minutes. Allow to cool for 5 minutes on the baking sheet before transferring to a wire rack to cool completely.

Once cookies are completely cool, frost them with the Vanilla Frosting. Note that the frosting begins to set quickly, so if you are adding sprinkles, sprinkle each cookie immediately after frosting it. Don't frost the whole batch of cookies and then try to sprinkle them, as the sprinkles won't stick.

Combine all ingredients for the frosting in a large mixing bowl. Using an electric hand mixer, whip until the frosting is smooth and fluffy. Mix in food coloring if desired.