Before grilling the potatoes, blanch them. Put the potatoes in cold water and add salt. Bring water to a simmer and cook the potatoes until they are tender.
Preheat a grill or grill pan on medium-high heat.
Slice the potatoes lengthwise and add to a large mixing bowl with the thyme, garlic, and olive oil. Season with gray salt and pepper and toss to coat the potatoes well. Grill the potatoes over indirect heat for about 3 to 5 minutes on each side until well marked and fully cooked.