In a medium bowl whisk together the flour, cocoa, baking powder and salt.
In a large bowl beat together the butter, shortening and sugar until fluffy.
Beat in the egg, egg white, vanilla, red food coloring and vinegar.
With the mixer on low speed, slowly beat in the flour mixture about 1/2 at a time.
Cover the bowl with clingfilm and refrigerate for at least 2 hours or overnight.
Preheat the oven to 350F degrees and line cookie sheets with parchment paper or silicone baking mats.
Form the dough into balls about 2 tablespoons in size and place 2 inches apart on the cookie sheets. Flatten slightly with your palm or the bottom of a glass dipped in flour.
Bake for 8-10 minutes or until the tops are just set.
In a large bowl beat together the cream cheese and butter.
Slowly beat in the powdered sugar about 1 cup at a time, then beat in the whipping cream as needed.
Frost the cooled cookies with knife and decorate with sprinkles.
*If you don't have cake flour, measure out 2 1/2 cups all-purpose flour. Then remove 1/3 cup of all-purpose flour and add 1/3 cup cornstarch. Sift the mixture 2 times.