In a double boiler over hot water melt chocolate with the butter. Remove from heat and allow to cool for 5 minutes. In an electric mixer add chocolate mixture and confectioners' sugar. Beat until mixture resembles chalky beads. Add the vanilla and the milk 1 tablespoon at a time until a spreadable consistency is reached. Beat until fluffy -- adding more milk if necessary.
Recipe courtesy of Lynn Kearney for Food Network Kitchens