Boil the potatoes: Place the cut potatoes in a large pot, cover with cold, salted water, and bring to a boil. Cook until just fork-tender but still firm (about 10-15 minutes). Drain thoroughly and let cool slightly.

Prepare the grill: Preheat your grill to medium heat (about 375°F to 400°F). Toss the slightly cooled, parboiled potatoes with 2 tablespoons of olive oil, salt, and pepper.

Grill the potatoes: Place the seasoned potatoes directly on the grill grates. Grill for about 5-7 minutes per side, turning occasionally, until they have nice char marks and are tender throughout. Remove from the grill and set aside to cool to room temperature.

Make the dressing: In a large bowl, whisk together the red wine vinegar, Dijon mustard, and a pinch of salt and pepper. Slowly drizzle in the remaining olive oil while whisking vigorously until emulsified. Then, whisk in the mayonnaise until smooth.

Assemble the salad: Add the cooled grilled potatoes, diced red onion, celery, fresh parsley, and chives to the dressing. Gently fold everything together until the potatoes are evenly coated. Taste and adjust seasoning if necessary.

Chill and serve: For best flavor, cover the salad and refrigerate for at least 1 hour before serving to allow the flavors to meld. Serve chilled or at room temperature.