Place the potatoes in a large pot with enough water to cover the potatoes by 1 inch. Add 2 tablespoons kosher salt. Bring the water to a boil over medium-high heat. Reduce the heat to a simmer. Let cook until the potatoes are fork tender, 8 to 10 minutes. Do not overcook, or your potato salad may be mushy. Drain and let cool while you whisk together the dressing.
In a medium bowl, whisk together the yogurt, mayonnaise, mustard, vinegar, garlic, salt, and pepper.
Transfer the potatoes to a large bowl and pour the yogurt mixture over the top. Add the celery, dill, chives, and parsley. Toss gently to combine.
Cover and refrigerate for at least 1 hour to allow the flavors to marry. Season with another big pinch of salt (the flavor of the salt gets absorbed as it sits), toss, then taste and season with additional salt and/or pepper as desired.
Notes
TO MAKE AHEAD: This red potato salad actually improves after a few hours in the refrigerator. You can prepare it up to 1 day in advance.
TO STORE: Refrigerate leftovers in an airtight container for up to 4 days.