Bring the water to a low boil. Add the sugar and stir until dissolved. Add the mint or peppermint extract and steep for 10-15 minutes (heat off or on low) until the syrup has good flavor to it. Remove the mint leaves and store in the refrigerator for future peppermint mochas. 🙂
Heat the milk and unsweetened chocolate together until melted (could be in the microwave or on the stovetop).
Add the milk mixture to a glass jar. Put a cap on the jar and wrap with a towel (the metal lid will get hot). Shake until foamy.
Pour the milk mixture into a mug. Stir in the coffee and 2-3 tablespoons of mint syrup. Top with whipped cream and candy cane pieces.