Combine milk and vanilla in a medium saucepan and heat over low heat until warm. Sift confectioners' sugar into milk mixture. Whisk slowly, until well combined. Remove the glaze from the heat and set over a bowl of warm water. Dip doughnuts into the glaze, 1 at a time, and set on a draining rack placed in a half sheet pan for 5 minutes before serving.
Recipe courtesy of Alton Brown, 2004