Using a clean finger run the rim of each mug with a small amount of corn syrup. Place crushed peppermint on plate. Press rim of each glass into crushed peppermint.
In large saucepan combine sugar, cocoa and pinch of salt. Add boiling water. Turn heat on to low and bring to simmer; stirring constantly. Simmer for 2-3 minutes; stirring constantly. Add milk and half n half. Stir to combine and simmer until warm; stirring frequently.
Remove from heat and stir in mint extract, Split between 4 mugs and top with whipped cream. Use candy canes for stir sticks.