Put the chocolate and sugar in a heavy-based saucepan. Pour in the milk, then add the vanilla extract and cinnamon.
Cover and gently heat, whisking once or twice, until the chocolate has melted. Continue heating until the mixture is steaming hot, but do not allow to boil. Stir in the Kahlua or other coffee liqueur, if liked.
Ladle the hot chocolate into 4 large cups or mugs and top with a few mini marshmallows. Serve immediately while steaming hot.