Boil the potatoes until they are fork-tender, approximately 25 minutes.
Remove the potatoes from water and allow them to cool slightly.
Meanwhile, combine the kosher salt, lime zest, and cayenne pepper in a small bowl. Mix well. Set aside.
Once the potatoes are cool enough to cut, slice into 6 wedges per potato. (Anything smaller will burn too fast on the grill!)
Brush the potato wedges with vegetable oil and place on the grill. Grill until golden in color, about 4-5 minutes. Flip the wedges, and grill for another 4-5 minutes.
Remove wedges from the grill, sprinkle lightly with lime juice, kosher salt mixture, and chopped cilantro.