Combine milk, sugar, and chocolate in a saucepan and cook, stirring frequently, until the chocolate is completely melted and smooth. Grating the chocolate into the pan (optional) speeds the melting process considerably.

Add the cornstarch and milk mixture and stir constantly over low heat for an eternity (this is the only way to prevent lumps) until thick enough to pour into two stemmed glasses. Top with whipped cream if desired.