Preheat oven to 350 degrees. Peel carrots and parsnips; halve crosswise to separate thick and narrow parts. Halve or quarter thick parts lengthwise (so pieces will be similar in size); cut both parts diagonally into 3/4-inch pieces.
On a large rimmed baking sheet, toss carrots and parsnips with oil, thyme, salt, and pepper. Spread in a single layer.
Roast vegetables until tender, tossing once or twice, 1 hour to 1 hour 20 minutes (if vegetables begin to stick to the pan, sprinkle with water, and loosen with a spatula). Serve immediately.
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