Preheat your oven to 325°F (163°C).
Season the beef short ribs generously with salt and pepper. In a large Dutch oven, heat the olive oil over medium-high heat. Add the short ribs in batches, browning them on all sides. Remove the ribs and set aside.
In the same pot, add the chopped onion, carrots, and celery. Sauté for about 5 minutes until the vegetables are softened. Stir in the minced garlic and cook for an additional minute.
Pour in the red wine, scraping the bottom of the pot to deglaze. Bring to a simmer and let it cook for about 5 minutes.
Stir in the beef broth, tomato paste, thyme, and bay leaves. Return the short ribs to the pot, ensuring they are submerged in the liquid.
Cover the pot with a lid and transfer it to the preheated oven. Braise for 2.5 to 3 hours, or until the meat is tender and falling off the bone.
Remove the pot from the oven and let it rest for 10 minutes. Discard the bay leaves before serving. Garnish with fresh parsley.