Preheat oven to 350. Prepare baking sheets by lining with parchment paper or silicone sheets.
In your mixer bowl, cream together the butter, shortening, sugar and powdered sugar about 3 minutes.
Beat in the eggs one at a time until the mixture is light and fluffy looking.
Add the milk and vanilla and mix for a minute.
In a large bowl, whisk together the flour, cornstarch, baking soda, cream of tartar and salt.
Add the flour mixture to the butter mixture and let the mixer stir until evenly combined.
Using a large cookie scoop to keep the cookies the same size, place a scoop of the dough in to your hand, gently form it in to a ball, then place on the prepared baking sheets.
Add about 1/4 cup granulated sugar to a bowl. Use the bottom of a glass sprayed with cooking spray to dip in the sugar and press down each ball to about 1/2 inch thick. (They will look crackly around the edges.)
Bake for 10-12 minutes until they are cooked, but not browned. (They will look a little puffy, but will cool perfectly.)
Remove the cookies from the oven and let them sit on the tray for 5 minutes. Then remove to a cooling rack.
Let the cookies cool completely before frosting.