Place the chocolate in the top of a gently simmering double boiler. Stir occasionally until melted, about 6 minutes.

Using a hand-held electric mixer or a standing mixer fitted with a paddle attachment, cream the butter until fluffy, about 2 minutes. Add the melted chocolate and beat to combine.

On low speed, gradually beat in the confectioners’ sugar. Add the salt and vanilla. Beat in 4 tablespoons of the milk, adding more milk if needed to reach spreading consistency.

Cover the surface of the icing with plastic wrap until you’re ready to frost the cupcakes.