This dish, prepared in a skillet, has all the qualities of a stew but takes only 10 minutes to make.
Trim any excess fat from the steak and slice the steak thinly. Salt and pepper each slice and dredge in flour. Heat a large, heavy frying pan, preferably cast iron. Add the olive oil, quickly sear both sides of the steak pieces (do not crowd the pan), and remove to a dish. Add the mushrooms to the hot pan, season with salt and pepper, and cook until soft. Remove from the pan and add to the platter. Add the onion and garlic to the hot pan and gently saute until soft and caramelized, about 10 minutes. Remove to the platter. Add the wine to the hot pan, turn up the heat, stir to deglaze, and cook until reduced by half. Add the beef broth and simmer for 2 minutes. Add the tomatoes and simmer for 5 minutes. Add the cooked mushrooms, onions, and garlic and simmer for 2 more minutes. Add the basil and beef and cook for several minutes, just to warm the beef thoroughly. Serve immediately.