Preheat your oven to 325°F (165°C).

Season the beef short ribs generously with salt and black pepper. In a large Dutch oven or oven-safe pot, heat the olive oil over medium-high heat. Add the short ribs and sear on all sides until browned, about 8-10 minutes. Remove the ribs and set them aside.

In the same pot, add the chopped onion, carrots, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5-7 minutes. Add the minced garlic and tomato paste, and cook for another 2 minutes.

Pour in the red wine and bring it to a simmer, scraping up any browned bits from the bottom of the pot. Let it simmer for 5 minutes to reduce slightly.

Add the beef broth, fresh thyme, rosemary, bay leaves, Worcestershire sauce, and balsamic vinegar to the pot. Stir to combine. Return the seared short ribs to the pot, submerging them in the liquid.

Cover the pot with a lid and transfer it to the preheated oven. Braise the short ribs for 2 1/2 to 3 hours, or until the meat is fork-tender and falling off the bone.

Remove the short ribs from the oven and let them rest for a few minutes. Skim any excess fat from the surface of the sauce. Serve the short ribs with the sauce, garnished with chopped fresh parsley.