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Wash and dry all produce. Dice potatoes into ½-inch pieces (for a smoother texture, peel potatoes first). Place in a large pot with half the thyme sprigs and enough salted water to cover by 2 inches. Bring to a boil and cook until tender, 15-20 minutes. Remove and discard thyme sprigs. Reserve ¼ cup potato cooking liquid, then drain and return potatoes to pot.