Mix together powdered sugar and cocoa powder and set aside. You can start with ½ cup of cocoa and add more at the end if you want a lighter chocolate taste.
Put the butter in a large bowl and beat with an electric mixer on medium speed until it is smooth and creamy. Mix in the vanilla.
Add the sugar/cocoa mixture to the butter/vanilla and beat well.
You can frost cake or cupcakes immediately.
Notes
Use whole milk for the creamiest textureYou can use other milks and milk substitutes, but the frosting may turn out thinner If you use unsalted butter, add ¼ teaspoon of salt to the batterFor a less chocolatey taste, reduce the cocoa powder to ½ cup