Preheat your oven to 325°F (163°C).
Season the short ribs generously with coarse kosher salt and freshly cracked black pepper.
In a large, oven-safe Dutch oven, heat the olive oil over medium-high heat. Add the short ribs and sear them on all sides until they develop a brown crust. This should take about 3-4 minutes per side. Remove the short ribs from the pot and set them aside.
In the same pot, add the chopped onions, carrots, and celery. Sauté them for about 3-5 minutes or until they begin to soften.
Stir in the tomato paste and add the rosemary, thyme sprigs, bay leaves, and red wine. Cook for a few minutes to let the wine reduce slightly.
Place the seared short ribs back into the pot, arranging them in a single layer. Pour in the beef stock until the ribs are mostly covered.
Cover the pot and transfer it to the preheated oven. Let the short ribs braise for about 2.5 to 3 hours, or until they are tender and can be easily pierced with a fork. Check occasionally and add more beef stock if needed to keep the liquid level consistent.
Once the short ribs are tender, remove them from the oven. Skim off any excess fat from the surface of the sauce.
Plate the short ribs, spoon the rich sauce over them, and garnish with fresh chopped parsley or thyme.