In a medium pot, cover the beets with cold water and boil until tender. Remove the beets and reserve for another use. Add the vinegar, sugar, turmeric if using golden beets, peppercorns and pickling spice. Boil, stirring occasionally until the sugar dissolves.
Remove the pot from the heat and let stand until the cooking liquid reaches room temperature. Add the eggs and onions. Cover tightly and refrigerate, turning the eggs occasionally, at least 8 hours and up to 24 hours. Remove the eggs from the liquid and serve.