I love eggs cooked in any and all ways, and first came across a similar recipe to this in a foodie group on Facebook. The pinkish-red hue on the surface of the peeled eggs deepen the longer they sit in the brine and absorb color from the beets. Adding onions is an adaptation to the original recipe and turned out to be a good idea because they add a crunchiness to the salad. The pungency of the onions is diminished and they actually are quite sweet and go well with the beets.
To hard-boil eggs, place them in a saucepan and cover with water. Boil for 10 minutes, remove from heat, cover and set aside to cool. Drain the eggs and cover with cold water before peeling.