Combine sugar and cornstarch in a small mixing bowl, mixing well. Add 1 cup milk, stirring well. Scald remaining milk in top of a large double boiler over simmering water. Add sugar mixture; cook 10 minutes, stirring constantly.
Gradually add boiling water and salt to melted chocolate; stirring until smooth. Add chocolate mixture to milk mixture in top of double boiler. Beat with a wire whisk until frothy. Serve immediately in mugs with a dollop of whipped cream.