Pat beef chuck roast chunks dry with paper towels to help achieve a good sear.
Heat olive oil in a large skillet over medium-high heat. Add beef chunks in batches and sear until browned on all sides.
In the same skillet, add chopped onion and cook until soft and translucent, about 5 minutes. Add minced garlic and cook for another minute until fragrant.
Transfer seared beef, sautéed onion, and garlic into the slow cooker. Pour in crushed tomatoes, beef broth, then stir in tomato paste, oregano, and basil. Season with salt and pepper and stir to combine.
Cover and cook on low for 7 to 8 hours or on high for 4 to 5 hours until beef is tender and sauce thickens.
About 20 minutes before ragu is done, bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente. Drain well.
Remove beef chunks from slow cooker and shred with two forks. Return shredded beef to the sauce and stir to combine. Adjust seasoning if needed.
Plate pasta and ladle beef ragu over the top. Sprinkle with grated Parmesan cheese and garnish with fresh basil leaves. Serve immediately.