1. Preheat oven to 450F.
2. Combine cilantro, chile, garlic, tomato paste, vinegar, paprika, cumin, brown sugar and 2 tablespoons oil in a small food processor. Pulse, scraping down the sides as needed, until pureed. Set aside.
3. Heat 2 tablespoons oil in a large cast-iron skillet over medium-high heat. Reduce heat to medium and add Brussels sprouts, sweet potato and teaspoon each salt and pepper. Cook, stirring often, until almost tender, 9 to 12 minutes.
4. Transfer to a plate.
5. Season steaks with the remaining teaspoon salt and teaspoon pepper.
6. Heat the remaining 1 tablespoon oil in the pan.
7. Add the steaks and cook until browned, about 1 minute per side.
8. Nestle the vegetables around the steaks in the pan. Top the steaks with half the reserved sauce.
9. Transfer to the oven and roast until the steaks are desired doneness, 8 to 10 minutes for medium. Stir the remaining sauce into the vegetables and serve them with the steaks.