Scrub the potatoes and cut them into approximately 1-inch chunks. Place them in a pot, cover with cold salted water, bring to a boil, then reduce to a simmer and cook for 12-18 minutes, until fork-tender but not falling apart; drain and cool.

Place the eggs in a saucepan and cover them with cold water. Bring the water to a boil, remove the pan from the heat, cover, and let the eggs stand for 10-12 minutes; transfer them to an ice bath and peel.

Cut the eggs in half and place the yolks in a bowl. Mash the yolks with the mayonnaise, yellow mustard, sweet pickle relish, apple cider vinegar or pickle juice, kosher salt, black pepper, and paprika.

Chop the egg whites and add them to a large bowl with the cooled potatoes, celery, and onion. Gently fold in the yolk dressing until everything is evenly coated, taking care not to break up the potatoes.

Cover the salad and refrigerate it for at least 1 hour. Before serving, sprinkle it with extra paprika and the optional chopped chives or green onions.