Think of this as hot chocolate for grown-ups—a rich and warming variation on kids’ cocoa. Add a splash of liqueur right before serving, if desired.
Melt the chocolate in a heavy saucepan (or a double boiler) over low heat, stirring constantly. Add the coffee, milk, and half-and-half and heat until hot (do not boil). Add the vanilla right before serving. Serve garnished with cinnamon sticks or nutmeg.