"Brown butter frosting is an 'old' recipe that is not commonly used anymore; however it is delicious. It is easy to make as long as you are careful to not burn the butter. This frosting is great on top of brownies."
Heat butter, stirring constantly, in a saucepan over medium-low heat until it browns and becomes very aromatic, 5 to 10 minutes. Whisk confectioners' sugar into butter until dissolved and remove saucepan from heat; stir in milk and vanilla extract.
Beat butter mixture using an electric mixer until frosting is smooth; add more milk if frosting is too thick.