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Preheat the oven to 450°F.
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Place the garlic halves on a sheet of foil.
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Set the thyme sprigs atop the garlic.
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Drizzle 1 tablespoon of oil over the garlic and thyme, and then wrap them tightly in the foil. Set the foil packet in a small baking dish and roast until the garlic is soft, about 35 minutes.
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Open the foil packet and continue roasting on the foil until the garlic is golden brown, about 10 minutes longer. Set aside.
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Meanwhile, toss the potatoes with 3 tablespoons of the oil on a large baking sheet then arrange the potatoes in a single layer and sprinkle with salt and pepper.
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Bake for 20 minutes. Using a metal spatula, turn the potatoes over.
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Drizzle with the remaining 3 tablespoons of oil.
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Continue baking until the potatoes are crisp and dark golden brown on all sides, about 25 minutes longer.
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Transfer the potatoes and thyme to a platter. Serve with the roasted garlic.