In a small saucepan, heat milk and cardamom over medium heat until steaming. Remove from heat and let steep for 15 minutes. Strain milk mixture through a fine-mesh sieve, discarding cardamom. Return spiced milk to pan.

Heat spiced milk over medium heat. Whisk in chocolate, cocoa, sugar, and vanilla, whisking until sugar has dissolved. Serve warm. Garnish with marshmallows, if desired.