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