In a large bowl, using an electric mixer, beat together cream cheese, butter, vanilla, and milk until smooth and fluffy.
Add cocoa powder and powdered sugar (one cup at a time) and continue to beat on low speed until frosting is smooth and the desired consistency. Add more powdered sugar or milk if needed: more sugar will thicken the frosting, milk will thin it.
Video
Notes
Yield: Makes 2 ½ cups, enough for thick frosting on a 9 x 13 inch cake, a 2 layer cake, or about 24 cupcakes (if you want to pipe frosting on cupcakes, make a double batch of frosting)
Storage: Frosting should be refrigerated or frozen. Thaw overnight in the fridge before using. Beat again briefly to restore texture. Frosted baked goods can be left out for a couple of hours but should be refrigerated for longer storage.
Photos depict use of dark cocoa powder, any type will work.