Sprinkle the potatoes with salt and pepper and toss with enough olive oil to coat. Grill the potatoes until caramelized, about 4 minutes per side. Place them on the top rack and close the grill, allowing them to finish cooking through, about 20 minutes more. Remove the potatoes from the grill and allow them to come to room temperature.
To make the vinaigrette, whisk together the vinegar, capers, honey, mustard and olive oil in a small bowl. Season with salt and pepper. Dice the potatoes into large chunks and toss in a bowl with the scallions and walnuts. Season with salt and pepper.
Dress the potatoes with enough vinaigrette to coat the salad. Top with the apples, chives, sesame seeds, cilantro and parsley and serve.