Preheat the grill. Preheat the oven to 325 degrees F.
Put the potato slices on the hot grill and cook for about 2 minutes on each side to mark them. Remove from the grill and place them in a single layer in a baking pan. Season both sides with salt and pepper. Add enough olive oil to reach 1/3 up the sides of the potatoes. Turn the potatoes over to coat with the oil. Scatter the thyme and garlic cloves over the potatoes, sprinkle with a little more salt, if desired, and place in the oven.
After about 15 to 20 minutes, the potatoes will be tender. Remove from the oven and let them cool in the oil. Serve at room temperature.
Chef's notes: Using a high quality olive oil will impart its flavor to the potato.