Dissolve and Boil: Bring the mixture to a rolling boil, stirring until the sugar/sweetener is completely dissolved. Remove from the heat.
Assemble the Jars: If using, tuck the sliced red onion pieces in and around the beets in the jars.
Pour and Seal: Pour the hot brine over the beets and onions, making sure the liquid fully covers the vegetables.
Cool and Chill: Gently tap the jars to release any air bubbles. Let the jars cool to room temperature, then seal tightly with lids.
Refrigerate: Place the pickled beets in the refrigerator. They will be ready to eat in about 24 hours, but their flavor will deepen over the next few days. They will last for up to 3 weeks in the refrigerator.