Fill a copper mule cup most of the way with crushed ice. To crush your own ice, place regular ice cubes in a double layer of gallon-sized zip-top bags and smash ice with a wooden rolling pin or a mallet until crushed. (After a tough day you may find you start preferring your cocktail with homemade crushed ice.) Stir in vodka, apple cider, ginger beer and lime juice. Garnish with apple slice and cinnamon stick.
I found Infuse Spirits vodka at Whole Foods and really liked it. You can use cinnamon vodka if you can't find apple cinnamon.