Season the short ribs generously with salt and pepper. In a large Dutch oven, heat the olive oil over medium-high heat. Add the short ribs and sear on all sides until browned, about 3-4 minutes per side. 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. Add the minced garlic and cook for an additional minute.
Stir in the red wine, scraping the bottom of the pot to deglaze. Bring to a simmer and let it reduce by half, about 10 minutes.
Add the beef broth, tomato paste, thyme, bay leaves, and the seared short ribs back into the pot. Bring to a gentle simmer.
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.
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 hot, garnished with fresh parsley. Enjoy with mashed potatoes or crusty bread to soak up the delicious sauce.
Notes
For a richer flavor, add a tablespoon of Worcestershire sauce to the braising liquid.
If you prefer a thicker sauce, remove the short ribs once cooked, and simmer the sauce on the stovetop until it reduces to your desired consistency before serving.