Melt chocolate in microwaveable bowl on high 30 seconds, stir. Microwave 30 seconds more, stir. Continue heating and stirring in 10-second increments until completely melted. Cool to room temperature. Stir in vanilla.
Using electric mixer, cream together butter, powdered sugar, and milk.
Add chocolate and continue beating until thoroughly combined, scraping sides as needed. Frosting should be light and fluffy.
Add more milk as necessary for desired consistency. (see notes)
Frosting consistency: frosting a cake should have easily spreadable frosting (add more milk). Piping cupcakes (or decorating) can use a stiffer consistency.