In a large skillet, heat olive oil over medium-high heat. Season the beef chuck roast with salt and pepper, then sear it in the skillet for about 4-5 minutes on each side until browned. Remove the beef and set aside.

In the same skillet, add the diced onion, carrot, and celery. Sauté for about 5 minutes until the vegetables are softened. Add the minced garlic and cook for an additional minute.

Stir in the crushed tomatoes, beef broth, tomato paste, oregano, basil, and red pepper flakes. Bring the mixture to a simmer.

Place the seared beef back into the skillet, cover, and reduce the heat to low. Let it cook for 4-6 hours, or until the beef is tender and easily shreds with a fork.

Once the beef is cooked, remove it from the skillet and shred it using two forks. Return the shredded beef to the sauce and stir to combine.

Meanwhile, cook the pasta according to package instructions. Drain and set aside.

Serve the shredded beef ragu over the cooked pasta, garnished with fresh parsley and grated Parmesan cheese.