Step 1

In a large heatproof bowl, microwave the butter and cocoa powder until butter is melted. Beat together with a hand mixer until smooth. Add the vanilla and milk and stir.

Step 2

Add the confectioners' sugar and stir, slowly at first, until incorporated; then beat on medium speed until frosting is smooth and creamy, about 1 minute. use immediately on cooled brownies, or store, covered at room temperature, for up to a day.