Trim the steak and pat it dry with paper towels.
In a small mixing bowl combine the oregano, paprika, salt, and black pepper.
Season the steak with the oregano mixture, pressing down to adhere to the steak; set aside for 20 minutes, or refrigerate for up to 24 hours.
In the meantime, heat 3 tablespoons olive oil in a large 12-inch skillet set over medium-high heat. To the heated oil add the bell peppers, onions, and garlic; season with salt and pepper, cover, and cook for about 8 to 10 minutes, or until softened.
Uncover, stir in the tomatoes and capers; continue to cook uncovered for about 5 minutes, or until slightly thickened.
Transfer the vegetables to a plate or bowl; cover and set aside.
Wipe down the skillet and return it to the burner.
Heat the remaining olive oil in the skillet over medium-high heat.
Lightly pat dry the flank steak with paper towels.
Add the steak to the heated oil and cook for 5 to 7 minutes per side, or until the internal temperature of the steak registers at 125˚F to 130˚F. Use an Instant Read Meat Thermometer to check for doneness. Transfer steak to a cutting board; cover loosely with foil and let rest for 8 to 10 minutes.
Add the chopped basil to the peperonata and stir until well combined.
Slice the steak thinly against the grain.
Taste the steak and peperonata for salt and pepper; adjust accordingly.
Arrange the sliced steak on a serving plate with the peperonata.
Garnish with basil.
Serve.