Add ginger to a small saucepan with two and a half cups water and simmer for 25 minutes. Let cool, then strain and set aside.

Mix honey with hot water in a large pitcher until dissolved. Add apple juice, cranberry juice, 1⁄2 cup ginger water, and cinnamon sticks. Let sit for a while to allow flavors to develop. Serve chilled, with cranberries for garnish.