Place steak in a medium bowl and sprinkle with flour; turn to coat. Heat oil in a large saucepan over medium-high heat. Add the steak (reserving excess flour) and cook, stirring once or twice, until browned on most sides and still pink in the center, about 3 minutes. Transfer to a plate and tent with foil to keep warm.dd mushrooms, onions and tomatoes to the pan and cook, scraping up any browned bits, until the vegetables have released their juices, about 3 minutes. Sprinkle the reserved flour over the vegetables; stir to coat. Add green beans, broth, wine, thyme, salt and pepper; increase the heat to high and bring to a boil, stirring often. Reduce heat to a simmer and cook, stirring often, until the broth has thickened, about 5 minutes. Add the steak and any accumulated juices and cook, stirring often, until heated through, about 2 minutes.