Wash and thoroughly disinfect the oranges, as the preserve is made with the peel (you can peel them if you prefer not to use the peel). In a pot, heat the water and mix it with the honey (do not let it boil). Let the mixture cool, then combine it with the apple cider vinegar.
Meanwhile, chop the ginger, cut the mint leaves, and break the cinnamon stick into smaller pieces.
Finally, in a glass jar, start layering all the ingredients: a bit of orange, then ginger, mint, cinnamon, and the syrup. Repeat the layers (orange, ginger, etc.) until all ingredients are used.
Place the jar in the refrigerator. It will be ready to eat in about 2 days, allowing the oranges to absorb all the flavors.