Combine olive oil, garlic, thyme, and salt in a small container. Set aside.

Place potatoes in a saucepan and cover with water. Bring to a boil and cook 8-10 minutes, until tender. Drain.

Toss olive oil and herb mixture with potatoes.

Place potatoes on aluminum foil and sprinkle with the Parmesan. Fold foil so edges meet.

Grill over medium high heat for about 20 minutes, rotating halfway through.