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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.
Heat grill to high.
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.