In a medium saucepan, heat the heavy cream and milk over medium-low heat. Chop the chocolate into small pieces and add it to the milk mixture, whisking constantly. Still whisking, add the cinnamon sticks, honey and brown sugar. Once the chocolate has completely melted, remove from the heat and add the vanilla and rum. Continue to whisk until a slight froth begins to form and everything is heated through. When ready to serve, remove the cinnamon sticks.
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