This is a real old family treat and one my Mom made every summer. And we are still treating ourselves whenever the beets are ready in the garden and they are ready now. A smooth vinegar and full of spices, sugar,vinegar, cinnamon and clove. here is the recipe https://www.rockinrs.com/CS-Pickled-Eggs.pdf

And as a side note the red on the eggs comes from the beets. If you leave everything in the brine long enough – good luck – the yolk of the eggs will turn red. Happy eating!