Heat the olive oil in a large skillet over medium heat. Season both sides of the steaks with salt and pepper. Cook in 2 batches if necessary. When the oil is hot and shimmering, add the steaks and cook, tuning each once, until seared and rich mahogany, about 6 minutes per side for medium-rare. Transfer the steaks to a plate.
Add the garlic to the pan and cook, stirring occasionally, until aromatic, about 1 minute. Pull the skillet from the heat, add the vinegar, and use a wooden spoon to scrape up any brown bits that cling to the pan. Stir in the oregano, butter, and any juices from the steak, until the butter melts. Add the greens to the skillet, season with salt and pepper, and toss until they begin to wilt, about 30 seconds.
Slice the meat against the grain into thin slices, divide between 4 plates, top with the greens and the pan juices. Serve.
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