Combine the oregano, 1 tsp salt and the 1/4 cup olive oil in a bowl. Rub the steak with the oregano and olive oil mixture on both sides and wrap tightly in plastic wrap. Refrigerate for at least 30 minutes or up to 24 hours.
Remove the steak from the refrigerator and bring to room temperature. Meanwhile, heat the 1/3 cup oil in a nonstick skillet over medium-high heat. Add bell peppers, onion, garlic, and 1/2 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.
Prepare your grill or heat an iron skillet until almost smoking. Sprinkle a little pepper on the steak and place on the grill. Cook steak 5-7 minutes on each side until internal temperature reaches 120 to 125 for medium rare. Remove steak from the grill or skillet and cover loosely with foil and rest for about 10 minutes.
Add the basil to the peperonata. Slice the steaks thinly across the grain. This is very important. Otherwise, the steak will be tough, but cut across the grain you'll have a steak that will melt in your mouth. Serve the steak with the peperonata.