Combine the milk, half-and-half and 2 of the cinnamon sticks in a small saucepan. Warm over medium-low heat, then stir in the chocolate discs. Stir until melted (though there will still be lovely particles of chocolate throughout). If it's too chocolatey for you, splash in a little more milk. If it's not quite sweet enough for you, add 1 teaspoon sugar.
Serve in mugs topped with toasted marshmallows, and place a cinnamon stick in each mug.