In the bowl of a stand mixer, combine butter, milk, vanilla extract and powdered sugar.
Mix on low to combine, then turn to medium speed until light and fluffy, 3 to 4 minutes.
Scoop half of the icing into a bowl and set aside.
To the icing in the mixer, add unsweetened cocoa powder and 1 tablespoon milk. Mix until combined.
Stir in drops of black icing color (found in most large craft stores, such as Michael’s and cake decorating stores) into the chocolate icing until it turns black. This will make enough icing for 16 cookies.