Combine all the spice rub ingredients in a small bowl.
Preheat all burners of a gas grill to medium-high heat or light a charcoal grill.
Cut the potatoes lengthwise into three-sided wedges. In a medium bowl, toss them with the olive oil, then sprinkle the cut edges with the spice rub (you may not need all of it).
If you're using a gas grill, lower one of the burners to low heat, leaving the other(s) at medium-high to create a hot zone and a cool zone. If you're using a charcoal grill, bank the hot coals to one side of the grill so that you have a hotter side and a cooler side. (The coals should be 5 to 6 inches from the grate on the hotter side.)
Put the potatoes on the grill, cut side down, directly over the hottest part of the fire. Cover the grill (if you're using a charcoal grill, cover it only partially and make sure the bottom vents are open). Cook the potatoes until deep reddish-golden brown, 4 to 6 minutes, and turn them over onto their other cut side. Cover and grill until nicely colored, another 4 to 6 minutes. Move the potatoes to the cooler side of the grill, flipping them so they're skin side down. Cover and grill until tender when pierced with a sharp knife, about another 6 minutes. Serve immediately.