Heat the milk in a medium pot over high heat until hot, but not boiling. Reduce the heat to very low and add the espresso, chocolate, sugar, and vanilla. Using a whisk, stir the mixture until the chocolate has melted. Continue to whisk the chocolate mixture until frothy every few minutes for about 8 minutes, until the chocolate has completely dissolved into the milk. Pour into mugs and serve immediately.
Recipe courtesy of Giada De Laurentiis