Sift together the flour, cornstarch, baking powder and salt into a large bowl and set aside.
In the bowl of an electric stand mixer whip together butter, shortening and sugar until it's fluffy, scrapping down the sides of the bowl as needed.
Add in the egg and mix until combined, then add the egg white, vanilla and vanilla extract and mix until combined.
With the mixer running, add the dry ingredients until just combined. Refrigerate for 2 hours
Preheat the oven to 375 degrees, scoop the dough out and roll into a ball. Lightly flour a surface an roll out the dough to ½ inch thick. Cut out your shapes and transfer to a cookie sheet. Bake for 11 minutes or until slightly brown.
After cooling, whip all the frosting ingredients together and frost the cookies