Parcook the potatoes: Place in a pot of water and boil until fork-tender; let cool. Slice each potato lengthwise into eighths.
Preheat a grill to medium or place a cast-iron grill pan over medium heat. Mix 1 tablespoon salt, the lime zest and cayenne in a small bowl.
Brush the potato wedges with the oil and season with salt and pepper. Grill until golden brown on all sides (including the skin) and just cooked through, about 1 1/2 minutes per side. Transfer to a platter; immediately season with the salt mixture and sprinkle with cilantro.