Make the dressing. In a sealable jar, combine the pickle brine, white wine vinegar, mustard, garlic, olive oil, salt, and pepper. Close the lid on top and shake vigorously. Check the dressing for seasoning and adjust if necessary. Set aside.
Place the potatoes in a medium saucepan and cover them with cold water. Cover and place the saucepan on the stove over medium-high heat and bring to a boil. Once boiling, remove the lid and lower the heat to a simmer. Cook until potatoes are just-tender, about 12-14 minutes. Drain the potatoes and allow them to cool just slightly.
Once the potatoes are cool enough to handle (but ideally still warm), cut them into quarters and transfer to a large bowl. Pour half of the dressing over the warm, cut potatoes, season them liberally with salt and pepper, and toss to combine. Let the lightly dressed potatoes sit until they are completely cool.
Once the lightly dressed potatoes are cool, add the red onion, fennel, celery, chopped dill pickles, fresh dill, parsley, the remaining dressing, and more salt and pepper. Toss to combine. Taste some of the salad to check for seasoning and adjust to your preference (more pickle brine, salt, pepper, dill etc).
This potato salad needs to sit for at least an hour to develop flavour. Cover the dill pickle potato salad and let it sit in the refrigerator for at least an hour before serving, and up to 5 days total.