Place the potatoes and 2 heaping tablespoons of salt in a large pot of water. Bring the water to a boil and cook until the potatoes are tender when forked, 10 to 15 minutes. Chop the potatoes into 1/2-inch pieces.
In a large bowl, add the potatoes, mayonnaise, parsley, mustard, celery, chives, onions and salt and pepper. Toss to coat the potatoes with the dressing and then add the eggs. Gently stir the potato salad, taking care not to mash the eggs. Serve immediately.