Scrub potatoes under cold running water; leave skins on. Slice potatoes into thick rounds and then brush both sides of potatoes liberally with olive oil. Place potatoes on grill and grill on both sides until slightly brown, about 2 minutes per side. Remove from the grill and place in a single layer on a baking sheet.
Drizzle potatoes liberally with olive oil again on both sides and then season both sides with salt and pepper. Place baking sheet on the grates of the grill and cook for about 10 more minutes, or until cooked through in the center and crispy on the outside. Remove from grill and sprinkle with minced garlic and chopped thyme leaves. Serve.