1) Combine all spices in a small bowl.
2) Place potatoes in a pot of cold water, add 1 tablespoon of salt and cook until potatoes are tender, but still firm, about 10 minutes. Drain, let cool and cut each potato lengthwise into 8 slices.
3) Heat griddle or barbecue to high.
4) Brush potatoes with oil and season with the Old Bay-style spice rub and grill until golden brown and cooked through, 3 to 5 minutes.