Cut the potatoes into ¾-inch chunks and place in a large pot with 2 teaspoons of kosher salt. Add enough cold water to cover the potatoes by about 1 inch. Bring to a boil, reduce to a gentle simmer, and cook until fork-tender, 8 to 10 minutes.

In a medium bowl, prepare the remaining ingredients: dice the hard-boiled eggs, pickle spears, and celery; mince the shallot; slice scallions; chop fresh herbs; and add remaining kosher salt, mayonnaise, mustard, and vinegar. Stir to combine.

Drain the potatoes and transfer to a rimmed baking sheet, spreading into a single layer. Sprinkle with remaining vinegar and let cool to room temperature, about 15 minutes.

Add the cooled potatoes to the bowl of dressing and fold to combine. Season with more salt and pepper as needed, cover, and refrigerate for at least 1 hour before serving.