Heat 2 tablespoons of olive oil in a large, heavy-based pot over medium-high heat.
Season the beef chunks generously with salt and pepper.
Add the beef to the pot, searing each side until browned. This should take about 5 minutes per side. Remove the beef from the pot and set aside.
In the same pot, add the diced onion, carrots, and celery. Cook until softened, about 5-7 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Pour in the red wine, stirring to deglaze the pot, scraping up any browned bits from the bottom. Allow the wine to reduce by half, which should take about 5 minutes.
Add the tomato paste to the pot and cook for 2 minutes to caramelize slightly.
Stir in the crushed tomatoes, beef broth, bay leaf, thyme, and oregano. Return the seared beef to the pot, nestling it into the sauce.
Bring the mixture to a simmer, then reduce the heat to low.
Cover the pot and let it simmer gently for 3-4 hours, or until the beef is tender and can be easily shredded with a fork.
If using a slow cooker, transfer the mixture to the slow cooker at this point and cook on low for 8 hours or on high for 4-5 hours.
Once the beef is tender, remove it from the pot and shred it using two forks.
Return the shredded beef to the pot and stir to combine with the sauce. Adjust seasoning with salt and pepper as needed.
Cook your pasta of choice according to package instructions. Drain and toss the pasta with the beef ragu.
Serve hot, garnished with freshly grated Parmesan cheese and chopped parsley or basil.