In a medium saucepan, combine milk, half-and-half and cinnamon. Stir over medium heat just until mixture boils. Add chocolate pieces and coffee crystals. Bring mixture back to boiling. Cook and whisk constantly until chocolate pieces are melted and mixture is smooth and well combined. Remove from heat; discard stick cinnamon. Stir in vanilla.
To serve, ladle hot mixture into warm mugs; top with whipped cream.