Place peeled hard boiled eggs in a quart-sized mason jar (or any other heatproof container of similar size).
In a medium saucepan, combine pickled beets, apple cider vinegar, water and brown sugar. Heat until it just comes to a boil.
Place the cinnamon sticks and cloves into the jar with the eggs.
Carefully pour the pickling liquid and beet slices into the jar with the eggs.
Tap the jar to help loosen any air bubbles and use a long, skinny spatula to ease out any remaining air bubbles. Place a lid on the jar.
Once it has cooled to room temperature, refrigerate. Let pickles rest at least 48 hours before eating.