Place candy canes in a glass container, and pour vodka over the candy. Cover and allow to sit at room temperature or in the refrigerator for 4-24 hours.
Place martini glasses in the freezer to chill.
In a cocktail shaker, add infused vodka, chocolate liqueur, and half and half. Add a few ice cubes, and shake for about 10 seconds. Immediately strain into chilled glasses. (You don’t want to shake or let the drink sit with the ice too long because it will become watered down.) Enjoy!
If you use a chocolate liqueur that is not cream based (like Godiva), you can double the half and half.