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© Meredith Corporation. All rights reserved. Used with permission.
Preheat oven to 450°F.
Combine onions, cabbage, 2 tablespoons oil, thyme and 1/2 teaspoon each salt and pepper in a large bowl. Transfer to a large rimmed baking sheet. Roast, stirring twice, until the vegetables are tender, 25 to 30 minutes.
About 10 minutes before the vegetables are done, pat steak dry and cut into 4 equal portions. Sprinkle with 1/4 teaspoon each salt and pepper. Heat the remaining 1 tablespoon oil in a large skillet over medium-high heat until very hot, but not smoking. Add the steaks and cook until browned on the bottom, 2 to 4 minutes. Turn over, reduce heat to medium-low and cook to desired doneness, 3 to 5 minutes for medium-rare. Transfer to a plate and loosely cover with foil.
Push the vegetables into 4 mounds. Sprinkle 2 tablespoons cheese on each and return to the oven until melted, about 2 minutes. Serve the steaks with the vegetables.