Clean the potatoes well, then cut into ½” pieces.
Bring a large pot of water to a boil, then salt generously. Cook the potatoes until fork tender. Drain and reserve.
While the potatoes are cooking, combine 1 cup of the mayonnaise, the Dijon mustard, pickle juice, and paprika in a large bowl.
When the potatoes are done, add them to the bowl with the mayonnaise mixture. Add the eggs, onion, pickles, and celery. Mix everything to combine. Season to taste with salt and pepper.
Cover and chill for at least 2 hours, but preferably overnight.
When ready to serve, remove from the refrigerator and stir in the remaining ⅓ cup of mayonnaise. Taste again, and season with more salt and pepper, if needed.
