In a medium pot, whisk together chocolate, cocoa, sugar and chile. Place pan over medium-low heat and whisk until chocolate begins to melt. Slowly whisk in milk, then cream. Drop in cinnamon stick. Bring to a simmer.
Remove pot from heat. Cover pot tightly and steep 1 hour. Whisk in vanilla and taste for sweetness, adding more sugar if you like. Warm over low heat before straining and serving hot, with marshmallows or whipped cream if desired.