Preheat your oven to 325°F (163°C).
Season the short ribs generously with salt and pepper. In a large Dutch oven, heat the olive oil over medium-high heat. Sear the short ribs on all sides until browned, about 3-4 minutes per side. Remove the ribs and set aside.
In the same pot, add the diced onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables are softened. Add the minced garlic and cook for an additional minute.
Stir in the tomato paste, cooking for another minute. Pour in the red wine, scraping up any browned bits from the bottom of the pot. Bring to a simmer and let it cook for about 5 minutes.
Add the beef broth, thyme, bay leaves, and the seared short ribs back into the pot. Bring the mixture to a gentle simmer.
Cover the Dutch oven with a lid and transfer it to the preheated oven. Braise for 2 ½ to 3 hours, or until the meat is tender and easily pulls away from the bone.
Once done, remove the pot from the oven. Discard the bay leaves and skim off any excess fat from the surface.
Serve the short ribs with the braising liquid spooned over the top and garnish with fresh parsley.