How to Make It
Heat 1 tablespoon of the oil in a large saucepan or Dutch oven over medium-high heat. Season the beef with ½ teaspoon salt and ¼ teaspoon pepper and cook, turning occasionally, until browned on all sides, 3 to 5 minutes. Transfer to a plate.
Heat the remaining tablespoon of oil in the saucepan over medium-high heat. Add the onion, carrots, garlic, rosemary, and ¼ teaspoon each salt and pepper and cook, stirring occasionally, until softened, 6 to 8 minutes. Add the tomato paste and cook, stirring, until slightly darkened, about 1 minute more.
Return the beef to the saucepan and add the chicken broth and tomatoes. Simmer, covered, stirring occasionally, until the beef is fork-tender, 60 to 75 minutes.
Add the mushrooms to the saucepan and cook, covered, stirring occasionally, until tender, 10 to 12 minutes more. If the sauce is too thin, simmer, uncovered, until thickened to the desired consistency.
Meanwhile, cook the pasta according to the package directions; drain and return it to the pot. Add the beef ragù and Parmesan and toss. Serve with additional Parmesan.