In a large pot, add the diced potatoes and cover them with cold water. Bring to a boil over medium-high heat and cook for about 10-15 minutes, or until the potatoes are fork-tender. Drain and let cool completely.
In a large mixing bowl, combine the mayonnaise, Dijon mustard, apple cider vinegar, salt, and black pepper. Mix until well combined.
Once the potatoes have cooled, add them to the bowl with the dressing. Gently fold in the celery, red onion, chopped hard-boiled eggs, and sweet pickle relish.
Stir everything together until the potatoes are well coated with the dressing. Taste and adjust seasoning if necessary.
Cover the potato salad and refrigerate for at least 1 hour before serving to allow the flavors to meld.
Before serving, sprinkle with fresh parsley if desired.