1. Cut steak lengthwise with grain into 3 equal pieces. Combine oregano and 2 teaspoons salt in bowl. Season steaks all over with salt mixture, wrap in plastic wrap, and refrigerate for at least 30 minutes or up to 24 hours.
2. Heat 1/3 cup oil in 12-inch nonstick skillet over medium-high heat until just smoking. Add red and yellow bell peppers, onion, garlic, and 1 1/4 teaspoons salt. Cover and cook, stirring occasionally, until vegetables are soft, about 10 minutes.
3. Stir in tomatoes and their juice, capers and brine, and pepper flakes. Continue to cook, uncovered, until slightly thickened, about 5 minutes. Season with salt and pepper to taste. Transfer peperonata to bowl, cover, and keep warm.
4. Wipe out skillet with paper towels. Pat steaks dry with paper towels and season with pepper. Heat remaining 1 tablespoon oil in now-empty skillet over medium-high heat until just smoking. Cook steaks until well browned and each registers 125 degrees (for medium-rare), 5 to 7 minutes per side. Transfer steaks to carving board, tent with aluminum foil, and let rest for 10 minutes.
5. Stir basil into peperonata. Slice steaks thin on bias against grain. Season steak slices with salt and pepper and drizzle with extra oil. Serve steak with peperonata.