Peel (or not) and cut the potatoes into bite-size cubes. Place the potatoes, 2 tablespoons of kosher salt, 2 tablespoons of apple cider vinegar, and 2 tablespoons of sugar in a large saucepan and cover with cold water by 2 inches. Stir well.
Bring the water to a boil, reduce to a simmer, and cook until the potatoes are tender, about 15-20 minutes.
Drain and transfer the potatoes to a large mixing bowl. Add 2 tablespoons of apple cider vinegar and the remaining 1 teaspoon kosher salt, stir vigorously to rough up the potato edges slightly, and cool to room temperature. While the potatoes cool, prepare the other ingredients.
Use a fork to mash 3 of the hard-boiled eggs and rough-chop the other 3 (set the 3 chopped eggs aside to add later).
In a different large mixing bowl, add the remaining 2 tablespoons of sugar, 2 tablespoons of apple cider vinegar, mashed eggs, chopped celery, onions, mayonnaise, relish (if using), mustard, black pepper, seasoned salt, paprika and parsley.
Gently fold in the cooled potatoes and remaining rough-chopped eggs.
If more salt and pepper are needed, add it now and stir gently. Keep in an airtight container in the fridge until ready to serve (1-24 hours).
When ready to serve, top with the sliced green onions for garnish.
