1. Preheat oven to 350 degrees.
2. Cream butter and sugars together until light and fluffy, about 3-4 minutes.
3. Mix in egg, vanilla extract, vinegar and red food color.
4. With the mixer on low speed, add flour, cornstarch, baking soda, dry pudding mix and cocoa powder.
5. Add milk, if needed. Dough will be thick.
6. Make balls of about 1 tbsp and then flatten a bit into thick discs and place on parchment lined cookie sheet, or use a silicon baking mat. They will spread a little while they bake.
7. Bake for about 7-8 minutes.
8. Remove from oven and allow to cool for 2-3 minutes on cookie sheet, then transfer to cooling rack to cool completely.
9. While cookies cool, make icing. Beat the cream cheese, butter and shortening until smooth.
10. Slowly add 3 cups of powdered sugar. Mix until combined.
11. Mix in the vanilla extract.
12. Add the rest of the powdered sugar and mix until smooth. Add water or milk until it's the right consistency.
13. Once cookies are cool, make cookie sandwiches and sprinkle with sprinkles.