Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain.
Meanwhile, season the steak with salt and pepper. Heat a large skillet over high heat until very hot. Add 1 tablespoon olive oil. Add the steak and cook until well browned, about 4 minutes per side for medium rare. Remove to a plate and tent loosely with foil.
Add the remaining 1 tablespoon olive oil to the skillet along with the bell peppers, red onion, garlic, oregano, red pepper flakes and 1/2 teaspoon salt. Cook, stirring, until the vegetables are softened, about 4 minutes. Reduce the heat to medium, stir in the wine and cook until almost evaporated, about 30 seconds. Add the tomatoes and 1/4 cup water. Bring to a simmer and cook until the sauce is thickened, about 5 minutes.
Add the pasta and any steak juices to the sauce; toss until warmed through, about 1 minute, adding the reserved cooking water as necessary to loosen. Season with salt and pepper and stir in 3/4 cup basil. Divide among bowls. Thinly slice the steak and serve on the pasta. Top with the remaining 1/4 cup basil.