Place the potato chunks in a large pot and cover with cold, heavily salted water. Bring to a boil over high heat, then reduce heat and simmer until potatoes are fork-tender, about 15-20 minutes. Drain immediately and let them cool slightly on a large baking sheet.

While potatoes are cooking, prepare the dressing: In a medium bowl, whisk together the mayonnaise, yellow mustard, apple cider vinegar, Worcestershire sauce, salt, and black pepper until smooth and fully combined.

In a very large bowl, combine the slightly warm (not hot) potatoes, chopped hard-boiled eggs, celery, and red onion.

Pour about two-thirds of the dressing over the potato mixture. Gently fold everything together using a rubber spatula, being careful not to mash the potatoes too much. Add more dressing as needed until the salad reaches your desired creaminess.

Stir in the sweet pickle relish. Taste and adjust seasoning, adding more salt or pepper if necessary.

Cover the potato salad and chill in the refrigerator for at least 2 hours, allowing the flavors to meld. Garnish with fresh parsley or chives before serving.