Heat 1 Tbs of butter and the oil over medium high heat in a skillet large enough to hold the vegetables in a single layer. Add the potatoes and carrots (and mushrooms if using). Cook partially covered, stirring periodically, until the vegetables are browned a bit on the outside and cooked through, 8-10 minutes. Add the onion and cook another couple of minutes, then add the garlic, peas and some salt and pepper. Stir it all together and cook another minute, then take it off the heat and set it aside, covered to keep warm.
In a second skillet, heat the other tablespoon of butter over medium high heat. While it's heating, salt and pepper the beef cubes, then add to the pan, again in a single layer so everything gets to the pan. Cook, stirring, about 3 minutes or so, just until the beef is browned and done to your liking. Put the beef in a serving dish.
Pour the wine and broth into the pan you cooked the beef and deglaze, stirring to scrape up any bits. Boil for just half a minute or less. Add the vegetables to the beef and stir to mix, then pour the sauce over it all.