Heat the heavy whipping cream to a slight simmer, add the chocolate pieces and slowly whisk until melted. Be careful not to scorch the cream. If it is too thick for your liking add milk to thin.
Add the cinnamon and cayenne pepper and continue to stir to incorporate completely.
Wet the rim of a small shot glass or cup with water and dip the rim into the crushed peppermint candy and pour the hot chocolate into each cup. Sprinkle the crushed peppermint candy of top and serve.