Cut the new potatoes into four pieces, roughly 1.5 inches each. There's no need to remove the skins. Boil potatoes in a medium-sized saucepan until they're soft enough that a knife will easily slice through them.
Meanwhile, in a medium-sized bowl mix together the onions, pickles, mayonnaise, mustard, celery, salt, and pepper.
Drain water from the boiled potatoes until they appear dried, place them in a large bowl, and add the mayonnaise mixture.
Add chopped boiled eggs to the potatoes and dressing. Mix gently (I use my hands) so as not to crush the potatoes. Garnish with parsley and serve hot or cold. If you don't serve warm, be sure to get this highly perishable dish into the refrigerator right away.
Notes
Courtesy of stacylynharris.com and Love Language of the South cookbook.