Melt butter in a small saucepan (or in the microwave using a microwave safe dish.) Stir in cocoa powder, mixture will form a thick paste.
Transfer chocolate mixture to a medium size mixing bowl. With mixer on low speed, add in powdered sugar, milk and vanilla.
Once ingredients are incorporated, turn mixer to medium high speed and beat about 5 minutes, until frosting is smooth and creamy. Spread on top of cooled cake.