In the bowl of a stand mixer, using a paddle attachment, cream the butter, cocoa, and vanilla at medium speed for 1 to 2 minutes. Add the powdered sugar one cup at a time, adding in milk whenever the frosting gets too stiff or the mixer starts to struggle. After the last of the powdered sugar has been added, add the rest of the milk and mix until the frosting is smooth and silky, about 2 minutes. For a stiffer consistency, add more powdered sugar, 1/4 cup at a time. If the frosting is too stiff, add in more milk, 1 tablespoon at a time.