1. Sprinkle the beef with ¼ teaspoon each of the salt and pepper. Heat 1 tablespoon of the oil in a large, heavy pot over medium-high heat and cool the beef until it is browned, about 5 minutes. Transfer the meat to a plate.
2. Add another tablespoon of oil to the pot, then add the mushrooms and cook until they release their liquid and begin to brown, 5 minutes. (Add a tablespoon or two of water to the pot if it seems too dry). Transfer the mushrooms to another plate.
3. Lower the heat to medium, add the remaining tablespoon of oil to the pot, then add the onion and cook until it is softened, about 3 minutes. Add the garlic and rosemary and cook, stirring, for 30 seconds. Stir in the tomato paste and then the wine. Bring to a boil and allow to reduce until the liquid is reduced by about half, 2 minutes. Add the broth, return the browned meat with any accumulated juices to the pot, and bring to a boil. Lower the heat to low, cover, and simmer for 1 hour. Place the farro in a bowl and add enough warm water to cover it. Let the farro soak as the stew simmers.
4. Once the meat is tender, drain the farro and stir it into the pot, then add the carrots, the mushrooms with their accumulated liquid, and the remaining ½ teaspoon of salt and ¼ teaspoon of pepper. Return to a boil and then simmer, covered, until the farro and the carrots are tender, 30-35 minutes more. Season with additional salt and pepper to taste. Serve garnished with the parsley.
5. The stew will keep in an airtight container in the refrigerator for up to 4 days, or in the freezer for 3 months.