In a medium saucepan, whisk together the milk, cocoa powder, and sugar. Place over medium heat and cook, stirring occasionally, for 3 to 4 minutes, or until smooth and heated through. Be careful not to let the mixture come to a boil.

Reduce the heat to low and add the dark chocolate. Whisk until the chocolate melts and the mixture is smooth, then add the vanilla and whisk to combine.

Pour into mugs and serve topped with whipped cream and chocolate shavings, if desired.