Place the quartered potatoes in a large pot and cover with cold, salted water. Bring to a boil, then reduce heat and simmer until fork-tender, about 15-20 minutes. Drain thoroughly and let cool slightly.

While potatoes cook, prepare the dressing. In a medium bowl, whisk together the mayonnaise, pickle juice, Dijon mustard, white vinegar, dried dill weed, and celery seed until smooth. Season generously with salt and pepper.

In a very large bowl, combine the slightly cooled potatoes, chopped dill pickles, diced celery, minced red onion, and chopped hard-boiled eggs.

Gently pour about two-thirds of the prepared dressing over the potato mixture. Use a rubber spatula to carefully fold the ingredients together until everything is lightly coated. Add more dressing as needed, ensuring not to overmix or mash the potatoes.

Taste and adjust seasonings one last time. Cover the salad and refrigerate for at least 2 hours (preferably 4 hours) to allow the flavors to meld.

Before serving, stir gently one final time and garnish with extra fresh dill or a few pickle chips, if desired.