Chop the chocolate as finely as possible.
Simmer milk and cinnamon sticks on low-medium heat for about 10 minutes. Stir occasionally. Don't let the milk boil.
Add in the chocolate, sugar, and pinch of salt. Stir continuously until the chocolate is melted and the mixture is smooth.
Pour mixture through a fine mesh sieve into a container with a spout (in order to make pouring easy).
Stir in bourbon.
Serve with lots of whipped cream, marshmallows or both!