Heat the grill to medium. 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 slice into 1/4-inch thick slices. Brush the potatoes on both sides with the oil and season with salt and pepper. Grill the slices until golden brown on both sides and just cooked through, about 10 minutes. Remove the slices to a platter in an even layer and immediately drizzle with the vinegar and season with salt.