Make the cookies.

In a medium bowl, whisk together the flour, cornstarch, cocoa powder, baking powder, and salt.  Set aside.

In the bowl of an electric mixer, combine the butter, shortening, and both sugars.  Mix on medium speed until light in color and fluffy.

Add the egg, egg white, vanilla, food coloring, and vinegar.  Mix until combined.

Reduce the mixer speed to low and slowly beat in the flour mixture (⅓ at a time).  Mix just until fully mixed.

Cover the bowl with plastic wrap and chill for 2 hours to overnight.

Preheat the oven to 350 degrees.  Line a baking sheet with parchment paper or a Silpat mat.

Use 2 tablespoons of dough and roll into balls.  Place the balls 2-inches apart on the prepared baking sheet.  Slightly flatten the balls with the bottom of a glass that has been dipped into flour or granulated sugar.

Bake for 8-10 minutes or until the tops are set and look dry, but the edges are NOT browned.

Cool the cookies completely on a wire rack.

Make the frosting:

Combine the cream cheese and butter in the bowl of an electric mixer.

Slowly beat in the powdered sugar, about 1 cup at a time, then adding 1 tablespoon of heavy cream as needed.

Once the powdered sugar has been incorporated, increase the mixer speed to high and beat until very fluffy.

Use an offset spatula to frost the tops of the cookies and decorate with sprinkles or cookie crumbs.