Combine the tomatoes (with their juices), tomato paste, onion, thyme, and 2 cloves of the garlic in a 4- to 6-quart slow cooker. Season the beef with ½ teaspoon salt and ¼ teaspoon pepper; place on top of the liquid. Cover and cook until the beef is tender, on low for 7 to 8 hours or on high for 5 to 6 hours (this will shorten total recipe time). Shred the meat, using 2 forks.
Combine the basil, lemon zest, oil, the remaining clove of garlic, and ¼ teaspoon each salt and pepper in a small bowl.
Twenty minutes before serving, cook the pasta according to the package directions. Serve the pasta topped with the beef ragù. Garnish with the basil gremolata and grated Parmesan.