Preheat the slow cooker if necessary; see the manufacturer's instructions. Put the chocolate and sugar in the slow cooker pot, then add the milk, vanilla extract and cinnamon.
Cover with the lid and cook on low for 2–3 hours, whisking once or twice, until the chocolate has melted and the drink is hot. Stir in the Kahlúa, if using. Ladle into mugs and top with a few mini marshmallows.