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Place a rack in the center of the oven. Preheat the oven to 375F. Lightly spray a 9 by 13-inch cookie tray with olive oil cooking spray.
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Put the potato wedges onto the prepared tray. Drizzle on 1 tablespoon oil. Sprinkle on 1/3 of the salt, 1/3 of the black pepper, the dried thyme, and the crushed garlic. Use your hands to toss so the potatoes are well-coated with oil and spices.
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Roast until the potatoes are tender and just starting to brown, about 12 to 15 minutes.
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Meanwhile, toss the broccoli with 1/2 tablespoon oil, 1/3 of the salt, and 1/3 of the black pepper.
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Remove the potatoes from the oven and flip each one. Add the broccoli to the same tray and roast for 5 minutes.
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Meanwhile, season both sides of the steak with the remaining 1/2 tablespoon oil, 1/3 of the salt, and 1/3 of the black pepper.
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Remove the tray from the oven and push the vegetables to the outside so there’s room for the steak in the center.
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Place a rack in the top 1/3 of the oven. Preheat the broiler.
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Put the tray into the oven on a rack in the top 1/3 of the oven under the broiler. Broil until the steak is done to your desired level of doneness, about 4 to 6 minutes per side, flipping once.