In a medium bowl, use an electric mixer to beat the butter on medium speed until it's smooth and creamy.
Add half of the powdered sugar and half of the cocoa powder, then beat for about 3 minutes.
Scrape the bowl and paddle, then add the remaining powdered sugar and cocoa powder. Beat for another 3 minutes.
Scrape the bowl and paddle, then add the milk and vanilla. Beat on medium-high speed until the mixture is light and fluffy.