In a flat glass dish, like a 3-cup Pyrex dish, place one layer of cooked, sliced beets.
Sprinkle over the top of the beets some of the minced ginger.
Drizzle over the beets and ginger a layer of balsamic vinegar.
Repeat layering the beets, ginger, and balsamic vinegar until all of the beets are used.
Finally, pour over the layers of beets either the orange juice or the pineapple juice. Cover and move to the fridge to marinate for at least four hours, preferably overnight.
Serve as a chilled side dish, or as an ingredient in salads, or as an ingredient in sandwiches. Enjoy!