Preheat the oven to 325°F (163°C).

Season the bone-in short ribs generously with salt and pepper on all sides.

In a large, oven-safe pot or Dutch oven, heat the olive oil over medium-high heat. Brown the short ribs on all sides, working in batches. Transfer the seared ribs to a plate.

Reserve 2 tablespoons of fat in the pot and discard the rest.

Return the pot to medium heat and add the chopped celery, carrots, and onion. Sauté until they begin to soften and the onion is translucent.

Add the minced garlic and tomato paste, stirring constantly until fragrant and slightly caramelized.

Pour in the red wine to deglaze the pot. Simmer for a few minutes to cook off the alcohol.

Stir in the beef broth, fresh rosemary sprigs, and bay leaves. Bring to a simmer.

Return the seared short ribs to the pot, ensuring they are fully submerged. Add more broth or water if needed.

Cover the pot and transfer it to the preheated oven. Braise the short ribs for about 3 hours, until tender and falling off the bone.

Remove the short ribs from the pot and set aside. Skim any excess fat from the braising liquid or use a fat separator.

Optionally, strain the liquid and return it to the pot. Simmer until reduced and slightly thickened into a flavorful sauce. Season with salt and pepper.

Serve the braised short ribs with the sauce spooned over them. Garnish with fresh parsley or rosemary. Pair with mashed potatoes, roasted vegetables, or creamy polenta. Enjoy!