Place the cubed potatoes in a large pot and cover with cold water. Add a pinch of salt and bring to a boil over medium-high heat. Cook until the potatoes are tender, about 10-15 minutes. Drain and let cool slightly.
In a large mixing bowl, combine the mayonnaise, Dijon mustard, apple cider vinegar, salt, and black pepper. Mix well until smooth.
Add the cooled potatoes to the bowl with the dressing and gently fold to coat the potatoes evenly.
Stir in the chopped celery, red onion, and hard-boiled eggs. Mix gently to combine all ingredients without breaking the potatoes.
Taste and adjust seasoning if necessary. Cover the salad and refrigerate for at least 1 hour to allow the flavors to meld.
Before serving, sprinkle with fresh parsley for garnish.