Mom served the eggs sliced.
Other than that, I don't remember much about them.
I figured that the color came from beets, but I wasn't sure about the method. I turned to the community at Serious Eats to see if anyone every heard of eggs like these, and the consensus was that they were soaked in the juice from pickled beets. Well, that made sense, My mother used to make pickled beets pretty often.
That's all I needed. So this is what I did:
Beet-Pickled Eggs (and pickled beets)
6 medium beets, cooked, peeled, and sliced
1/2 medium onion, sliced
1 1/3 cups water
1 cup vinegar
1 tablespoon sugar
1 teaspoon salt
Put the eggs, beets, and onion in a non-reactive bowl. Heat the vinegar, water, sugar and salt to boiling. Pour this over the beets and eggs in the bowl. If the liquid doesn't cover the ingredients, add more vinegar and water, as needed.
Let the mixture come to room temperature, then refrigerate overnight. The next day, you'll have a ring of purple surrounding the bright white. If you leave the eggs soaking longer, the color will penetrate further. It's up to you.
After you pull out the eggs, the beets and onions can be served alongside the eggs or separately. Or, if you have juice left over from pickled beets, use that rather than making a fresh batch of pickled beets.
You can serve the eggs simply sliced, but in this case I decided to make deviled eggs with them. Use your favorite recipe. My typical add-ins are mayonnaise to the get texture I'm looking for, mustard and sweet pickle relish - just a little for the the tartness of mustard and sweetness of pickles, and then just a hint of horseradish for a little kick.