Place the potatoes in a large pot of cold water, add 2 tablespoons of salt and cook until potatoes are tender, but still firm, about 15 minutes. Drain and let cool slightly.
Heat the grill to high.
While the potatoes are cooling, heat 2 tablespoons of the oil in a small saute pan on the grates of the grill. Add the garlic, thyme and chili flakes and cook until the garlic is just soft, about 45 seconds. Remove from the heat.
Slice each potato in half lengthwise then slice each half into 3 or 4 wedges, depending on the size. Brush the wedges with the remaining 3 tablespoons of oil and season with salt. Grill until lightly golden brown and just cooked through, about 6 minutes. Remove to a platter and immediately toss with the garlic mixture and chopped parsley.