Place the cubed potatoes in a large pot and cover with cold water. Bring to a boil over high heat, then reduce to a simmer and cook for 10-12 minutes until tender but not mushy. Drain and let cool slightly.

In a medium bowl, whisk together mayonnaise, Dijon mustard, sweet pickle relish, salt, pepper, and paprika until smooth and well combined.

In a large mixing bowl, combine the cooled potatoes, chopped red onion, diced celery, chopped hard-boiled eggs, and fresh parsley.

Pour the dressing over the potato mixture and gently fold everything together until evenly coated. Be careful not to overmix to keep the potatoes intact.

Cover the bowl and refrigerate for at least 1 hour to allow the flavors to meld. Stir gently before serving and adjust seasoning if needed.