Place the butter in a saucepan over medium-high heat. Cook, stirring constantly, until the butter is a nice tan color. If it gets dark brown or black you have allowed it to burn too long. When butter has been "burned" remove the saucepan from the heat.
Slowly mix in confectioners' sugar and vanilla. Beat on high speed of an electric mixer until light and fluffy. Beat in the milk a tablespoon at a time until desired spreading consistency is achieved. Use frosting immediately, as this frosting will set up quickly.