1In a medium saucepan, melt chocolate in milk over medium-low heat. Remove from heat, and let stand for 2 minutes. Whisk the chocolate until melted and smooth.
2Stir in the eggnog, and heat gently over low heat until very warm but not boiling. Remove from heat, and stir in the vanilla and coffee liqueur. Pour into mugs, and serve with whipped cream and a cinnamon stick garnish.