Browned Butter Frosting

Cook the butter in a small heavy saucepan over medium heat, stirring constantly, for 6 to 8 minutes or until the butter begins to turn a golden brown. Immediately remove the pan from the heat. Pour the butter into a bowl. Cover and refrigerate for 1 hour or until the butter cools and begins to set.Beat the butter on medium speed with an electric mixer until fluffy; gradually add the powdered sugar alternately with the milk, starting and ending with the sugar. Beat on low speed until smooth after each addition. Add vanilla.