In a saucepan, over low heat, melt butter. Stir in cocoa powder. Mixture will resemble a thick paste.
Transfer chocolate mixture to a the bowl of a stand mixer. With mixer on low speed, add in powdered sugar and milk, alternating the two. Reserve a few tablespoons of milk. If frosting is thick, add in remaining milk. Add vanilla extract.
Turn mixer to medium high speed and beat about 5 minutes, until frosting is smooth and creamy.