Place the potatoes in a large pot and cover with an inch of cold water. Add 2 teaspoons salt and bring to a boil. Let simmer until the potatoes are fork tender, about 20 minutes. Drain and let cool until cool enough to handle but still warm.

In a large mixing bowl, whisk together the pickle juice, olive oil, 2 teaspoons salt and 1 teaspoon pepper. Add the pickles, onion, and celery. Stir to combine.

Cut the potatoes in half, add to the mixing bowl, and stir to combine. Let sit for a few minutes.

In a small bowl, combine the mayonnaise and mustard. Add the eggs to the potatoes, then the mayonnaise/mustard sauce, and gently stir to combine. Cover and refrigerate for at least 1 hour. Taste and adjust seasoning with more salt and pepper, if desired. Can be made a day ahead.

Garnish with paprika before serving.