In a large mixing bowl, combine butter and sugar. Beat until light and fluffy.
Beat in egg yolk, milk, vanilla, and red food color.
In a small bowl, whisk together flour, cocoa, and salt.
Add dry ingredients to the wet ingredients in the mixing bowl, and beat until just combined.
Refrigerate for 1 hour or until dough is easy to handle.
Shape into 1-inch balls.
Roll each ball in sprinkles, thoroughly coating.
Arrange two inches apart on parchment paper or silicone mat-lined baking sheets.
Press an indentation in the center of each dough ball using your thumb or the end of a wooden spoon.
Bake at 350 degrees for 10-12 minutes, or until cookies appear set.
Remove from heat, and if desired, repress the indentation while cookies are still warm.
Remove cookies to wire racks to cool completely.
Meanwhile, prepare cream cheese frosting.