Preheat oven to 425 degrees. Toss potatoes with oil; season with salt and pepper. Arrange in a single layer on 2 rimmed baking sheets. Roast, flipping halfway through, until tender and golden, about 30 minutes.
Preheat broiler with rack 6 inches from heating element. Transfer potatoes to a 9-by-13-inch baking dish. Toss with thyme; top with cheese. Broil, rotating pan, until cheese is bubbly, about 2 minutes. Serve warm.