Place the whole potatoes in a large pot and cover with water. Stir in 1 tablespoon salt.
Bring to a boil and cook for about 25 minutes, or until the potatoes are fork-tender.
While the potatoes are cooking, prepare the dressing. In a large mixing bowl, combine the mayonnaise, mustard, salt, pepper, and paprika. Place the bowl in the refrigerator to chill until the potatoes are ready.
Drain the cooked potatoes and allow them to cool just enough to handle.
Peel off some of the potato skins, leaving portions of the skin on for extra texture and flavor.
Dice the potatoes into bite-sized pieces and add them to the chilled dressing.
Add the green onions, chopped pickles, 4 chopped egg whites, and 1 whole egg chopped.
Using a rubber spatula, gently fold everything together until evenly coated. Be careful not to overmix, as the potatoes can break apart before it's cooled.
Taste and adjust seasoning if needed.
Cover and refrigerate for at least 1 hour before serving. For the best flavor, chill for several hours or overnight.