For the hot chocolate with chestnut topping, mash the chestnuts in a small bowl with a fork and stir with the rum until smooth. Whip the cream until creamy and stir a third of it loosely into the chestnut mixture. Now carefully fold the chestnut mixture into the cream and chill.
For the hot chocolate, bring the milk to a boil in a saucepan, remove from heat, stir in the honey, season with vanilla and cardamom, and whisk in the coarsely chopped dark chocolate until completely melted. Pour the hot chocolate into (preheated) mugs, pour the chestnut cream into a piping bag and pipe it into the chocolate. You can also use two large spoons to prick out small balls of the cream and gently place them in the chocolate.
Sprinkle the hot chocolate with chestnut topping with cinnamon or cocoa powder as desired and enjoy hot. Just right for cold autumn and winter evenings!