Begin by preparing the potatoes for the salad. Peel and chop them into bite-size cubes, ensuring they are similar in size for even cooking. In a large pot, bring cold water to a boil over high heat, then reduce to a simmer. Add the chopped potatoes and cook for about 10-12 minutes until fork-tender.
While the potatoes are cooking, take this time to prepare the creamy dressing for the salad. In a separate bowl, whisk together the mayonnaise, dill pickle relish, sugar, dried parsley, red onions, McCormick celery salt, smoked paprika, black pepper, dried celery flakes, mustard, and apple cider vinegar until well combined.
Once the potatoes are cooked, drain them and let them cool for a few minutes. In a large bowl, combine the potatoes with the prepared dressing, ensuring all the potatoes are evenly coated.
To allow the flavors to develop and meld together, cover the potato salad with plastic wrap and refrigerate for at least an hour before serving. When ready to serve, garnish with additional parsley if desired.