1. Heat oven to 450. Cook the pasta according to the package directions. Reserve 1 cup of the cooking liquid, drain the pasta and return it to the pot.
2. Meanwhile, on 2 large rimmed baking sheets, toss the cauliflower, Brussels sprouts, and onion with the thyme, 2 tbsp. of the oil, and 1/2 each tsp. salt and pepper. Roast, tossing the vegetables once and rotating the sheets halfway through, until golden brown and tender, 15-20 minutes.
3. Add the vegetables, pecorino, 1/2 cup of the reserved cooking water, and the remaining 2 tablespoons of oil to the pasta and toss to combine (add more cooking water if the pasta seems dry). Serve sprinkled with additional pecorino.
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