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PdfCombine oregano and 1 tsp salt in bowl. Cut steak with grain into 3 equal pieces. Sprinkle steak with oregano mixture, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes or up to 24 hours.
Heat ⅓ cup oil in 12 inch nonstick skillet over medium-high heat until just smoking. Add bell peppers, onion, garlic, and ½ tsp salt. Cover and cook, stirring occasionally, until vegetables are soft, about 10 minutes.
Stir in tomatoes and their juice, capers and brine, and pepper flakes and cook, uncovered, until slightly thickened, about 5 minutes. Season with salt and pepper to taste. Transfer peperonata to bowl, cover, and keep warm.
Wipe skillet clean with paper towels. Pat steaks dry with paper towels and season with pepper. Heat remaining 1 tbsp oil in now-empty skillet over medium-high heat until just smoking. Cook steaks until well browned and meat registers 120 to 125 degrees (for medium-rare), 5 to 7 minutes per side. Transfer steaks to carving board, tent loosely with aluminum foil, and let rest for 10 minutes.
Stir basil into peperonata. Slice steaks thing against grain on bias. Season steak slices with salt and pepper and drizzle with extra oil. Serve steak with peperonata.