Season the beef short ribs with salt and pepper.
In a large Dutch oven, heat the olive oil over medium-high heat. Add the short ribs in batches, browning on all sides.
Remove the browned short ribs from the Dutch oven and set aside.
Add the onion, carrots, and celery to the pot; cook until softened, about 5-7 minutes. Add the garlic and cook for another minute.
Deglaze the pot with red wine, scraping up any browned bits stuck to the bottom.
Stir in the crushed tomatoes, tomato paste, oregano, thyme, and reserved short ribs into the pot.
Bring the mixture to a gentle simmer, then cover and reduce heat to low. Cook for 4-5 hours.
Check the meat after four hours; it should be fork-tender. Adjust seasoning if needed.
Once done, remove the short ribs, shred the meat, and discard bones and excess fat.
Return the shredded beef to the pot and stir to combine. Simmer for an additional 15-20 minutes.
Serve the ragu over cooked pasta or polenta and sprinkle with fresh parsley.