Cook butter in a small heavy saucepan over medium heat, stirring constantly, 6 to 8 minutes or until butter begins to turn golden brown. Remove pan from heat immediately, and pour butter into a small bowl. Cover and chill 1 hour or until butter is cool and begins to solidify.
Beat butter at medium speed with an electric mixer until fluffy; gradually add powdered sugar alternately with milk, beginning and ending with powdered sugar. Beat mixture at low speed until well blended after each addition. Stir in vanilla.
Spread cupcakes evenly with Browned Butter Frosting; garnish with fresh mint leaves and edible violas, if desired.