Chocolate Cookie Icing

Put chocolate in a small, deep heatproof bowl. Set a fine sieve by the bowl. Put milk in a 2-cup microwave-safe glass measuring cup and microwave on High just until it begins to boil and foam up the sides, 40 to 60 seconds. Pour half the hot milk through the sieve onto the chocolate and let stand without stirring for about 2 minutes to soften the chocolate. Stir vigorously until smooth and the chocolate is mostly melted.

Pour the remaining milk through the sieve into the bowl. Add vanilla. Stir vigorously until smooth. Sift sugar onto the mixture and stir in thoroughly.

Use the icing as is for drizzling or let cool until thick enough to be piped or spread. To use as a filling for thumbprints, refrigerate until very cold and stiff.