Peel and core the apples. Cut them in half and then into thin slices. In a large skillet, heat the honey over low heat until it begins to foam and turns a very light brown, about 5 minutes. Remove the skillet from the heat and add the ground cinnamon and apple slices. Return the skillet to medium heat and cook, stirring from time to time with a wooden spoon, until the apples are soft, 30 to 35 minutes.
While the apples are cooking, flavor the cider: In a medium saucepan, combine the cider, cinnamon sticks, cloves and vinegar and bring to a simmer over high heat. Cook until the liquid is reduced by half, 10 to 12 minutes.
Make the jam: Strain the cider mixture over the cooked apples (discard the cinnamon sticks and cloves). Simmer the apples over medium heat until all of the flavors meld and the liquid is almost completely absorbed, 5 to 8 minutes. Add the lemon zest and juice. Remove the skillet from the heat and set it aside to cool. Divide the jam among jars and refrigerate for up to 2 weeks.