To make the hot chocolate:

1. In a medium sized saucepan over medium heat, add the milk, cinnamon stick, vanilla and peppermint extracts.  Heat the milk until steaming and slightly frothy.
2. Lower the heat to medium low so that the milk continues to steam but not bubble to allow the flavors to infuse.  Cook for about 10 minutes.
3. Remove the cinnamon stick and whisk in cocoa powder.  Bring the temperature up to medium, and cook until the mixture is steaming and frothy.
4. Remove from heat, and strain through a sieve into a medium bowl.  Clean out the saucepan so no bits of cocoa remain.  Return the strained cocoa milk mixture to the saucepan.
5. Over medium heat, gently stir in the chocolate pieces. Keep stirring until you have reached your desired thickness, about five minutes
6. Whisk in a pinch of salt and up to a tablespoon* of sugar. Taste the hot chocolate. If you find it’s too rich or bitter, stir in a tablespoon or two of half and half cream.  
7. Remove from heat, and pour into two small cups.
8. Garnish with crushed candy cane or whipped cream.