Heat a large Dutch oven over medium-high heat. Add oil; swirl to coat.
Sprinkle ribs with a strong pinch each of sea salt and freshly ground black pepper.
Add the ribs to pan; cook 10 minutes, until they've browned on all sides
Transfer the ribs to the slow-cooker
To the dutch oven, add the onion, carrot, celery, and garlic; cook ~ 5 minutes, stirring occasionally.
Add the beef broth, wine, soy sauce, Worcestershire, tomato paste, basil, oregano, and tomatoes, gently breaking up tomatoes with a spoon.
Add the tomato mix to the cooker, along with the ribs.
Cover and cook on LOW for 7 ½ hours
Remove the ribs and discard the bones. Shred the beef with two forks.
Add the shredded beef, along with another pinch each of sea salt and freshly ground black pepper back into the slow-cooker.
Increase the heat to HIGH and cook, covered for 30 minutes
Cook pasta according to the package directions
Serve beef mixture over pasta, topped with parsley and grated Parmesan