Meanwhile, preheat a large cast-iron griddle on the grill. In a bowl, toss the potatoes with the remaining 1/4 cup of oil and season with salt. When the griddle is very hot, add half of the potatoes in a single layer, cut sides down. Cook them over high heat until browned, 10 minutes. Turn the potatoes and cook until the skins are browned in spots, 5 minutes longer. Transfer the potatoes to a platter. Cook the remaining potatoes. Alternatively, preheat the oven to 425°. Arrange the potatoes cut side down on 2 baking sheets. Roast for about 25 minutes, switching the position of the pans halfway through, until the potatoes are browned.