Cut 2 pounds red potatoes or Yukon Gold potatoes into ¾-inch chunks (peel first if desired). Place the potatoes and 2 teaspoons of the kosher salt in a large pot. Add enough cold water to cover the potatoes by about 1 inch. Bring to a boil over high heat. Reduce the heat to maintain a gentle simmer, and cook until the potatoes are fork-tender, 8 to 10 minutes.

Meanwhile, prepare the following, adding each to the same medium bowl as you complete it: Peel and dice 3 hard-boiled large eggs if using; dice 2 dill pickle spears (about ⅓ cup, or measure out ¼ cup sweet pickle relish) and 2 medium celery stalks (about ¾ cup); mince 1 large shallot (about ¼ cup); thinly slice 2 medium scallions if using (¼ cup); finely chop ¼ small bunch fresh parsley, dill, or a combination until you have 2 tablespoons; add remaining ½ teaspoon kosher salt, ½ cup mayonnaise, 1 tablespoon Dijon mustard, and 1 tablespoon of the apple cider vinegar or rice vinegar, and stir to combine.

Drain the potatoes well in a colander, then transfer the potatoes to a rimmed baking sheet and spread into a single layer. Sprinkle the remaining 1 tablespoon vinegar evenly over the potatoes. Let cool to room temperature, about 15 minutes.

Add the potatoes to the bowl of dressing and fold to combine. Taste and season with more kosher salt and black pepper as needed. Cover and refrigerate for at least 1 hour or up to 1 day before serving.