Boil the potatoes in a large pot for approximately 20 minutes or until a fork tender. Drain the potatoes and set aside to cool for approximately 5 minutes. Remove the skins from the potatoes (the potatoes will still be warm to the touch when you peel them), and place the skinned potatoes in a large bowl. Run a knife through the potatoes to coarsely chop them. Add the celery, pickles, onions, parsley, salt and pepper to the potatoes and toss. Fold in the mayonnaise to coat well. You’ll end up with a creamy potato salad that still has some soft chunks of potatoes.