Because flat-iron steaks are well marbled, there's no need to add oil to the skillet. When cooked up to medium, they remain tender and juicy. Our stir-together mustard sauce is another delicious accompaniment.
Heat a large cast-iron or other heavy-bottomed skillet over medium-high until very hot. Season steaks with salt and pepper. Add to skillet; sear 4 to 8 minutes per side for medium-rare (if browning too quickly, reduce heat after turning steaks). Transfer steaks to a plate, and cover loosely with aluminum foil (reserve skillet).
Add wine to skillet; simmer over medium-high, stirring occasionally and scraping up browned bits with a wooden spoon, until syrupy, 4 to 6 minutes. Remove skillet from heat. Stirring constantly, drop butter into sauce, one piece at a time, waiting for each piece to blend in before adding the next. Season with salt and pepper. Serve steaks drizzled with sauce.