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1. Adjust oven rack to middle position and heat oven to 350 degrees. Pat steaks dry with paper towels and season with salt and pepper. Heat 1 tablespoon oil in large skillet over medium-high heat just until smoking. Brown steaks, about 3 minutes per side, then transfer to wire rack set inside rimmed baking sheet. Roast steaks until meat registers 125 degrees (for medium-rare), about 10 minutes. Transfer steaks to serving platter, tent with foil, and let rest while preparing sauce.
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2. While steaks are in oven, add mushrooms, onion, 1/4 teaspoon salt, and remaining oil to empty pan and cook until softened, about 8 minutes. Add garlic, oregano, and sun-dried tomatoes and cook until fragrant, about 30 seconds. Add vinegar and cook, scraping up any browned bits with wooden spoon, until thick and syrupy, about 1 minute. Transfer mushroom mixture to bowl; set aside.
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3. Add drained diced tomatoes to empty pan and cook until deep red and dry, about 3 minutes. Stir in roasted peppers, reserved tomato juices, and mushroom mixture. Reduce heat to medium-low and simmer until sauce is no longer watery, about 5 minutes. Off heat, stir in basil and season with salt and pepper. Spoon sauce over steaks. Serve.
