Make a simple syrup infused with the cinnamon stick by combining 1/2 cup water, 1/2 cup sugar and the cinnamon sticks in a small pot. Heat over high heat until the sugar melts. Remove from heat and let cool.
In a cocktail shaker with ice, combine vodka and cranberry juice with simple syrup to taste. Shake and strain into a chilled cocktail glass, top with a splash of hard cider and garnish with a very thin slice of apple floating on top.