Combine oregano and 1 teaspoon salt in bowl.
Cut the steak with the 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 oil in 12-inch nonstick skillet over medium-high heat until just smoking.
Add bell peppers, onion, garlic, and ½ teaspoon salt.
Cover and cook, stirring occasionally, until vegetables are soft, about 10 minutes.
Add the tomatoes, capers and brine, and pepper flakes.
Cook, uncovered, until slightly thickened, about 5 minutes.
Transfer peperonata to bowl, cover, and keep warm.
Pat steaks dry 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 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.
Add basil into peperonata.
Slice steaks thin against grain on bias.
Serve steak with peperonata.