Place the potatoes in a large pot and cover with cold water. Add 1 tablespoon of salt to the water. Bring to a boil, then reduce to a simmer. Cook for 10–12 minutes, or until the potatoes are just fork-tender. Do not overcook.
Drain the potatoes and spread them out on a baking sheet to cool slightly. Letting them steam off excess moisture helps the dressing cling better.
In a large mixing bowl, whisk together the mayonnaise, mustard, apple cider vinegar, and relish until smooth. Taste and adjust seasoning with salt and pepper.
Add the cooled potatoes to the bowl. Gently fold them into the dressing, being careful not to mash them.
Stir in the chopped hard-boiled eggs, celery, and red onion. Mix just until everything is evenly coated.
Cover and refrigerate for at least 1 hour before serving. Chilling allows the flavors to meld beautifully.
Just before serving, garnish with paprika and fresh parsley for color.