Prepare Pickled Eggs. Combine the vinegar, water, sugar, and 2 medium beets, peeled and grated on the large holes of a box grater in a saucepan. Simmer, covered, for 5 minutes, then strain out the beets. Return the liquid to the pan and add the onion, garlic, pickling spice, and salt. Simmer 5 minutes more and pour over the eggs. Proceed as directed.