Pat the short ribs dry with paper towels and season generously with salt and pepper. Heat olive oil in a large Dutch oven or oven-safe pot over medium-high heat. Sear the short ribs in batches until deeply browned on all sides, about 3-4 minutes per side. Remove the ribs and set aside.

Add the chopped onion, carrots, and celery to the same pot. Sauté over medium heat until softened, about 5-7 minutes. Add the minced garlic and tomato paste, cooking for another 1-2 minutes until fragrant.

Deglaze the pot with red wine, scraping up any browned bits from the bottom. Bring to a simmer and cook for 5 minutes, allowing the alcohol to evaporate.

Stir in the beef broth and diced tomatoes. Return the seared short ribs to the pot, nestling them among the vegetables. Add the fresh rosemary, thyme, and bay leaves. Bring the liquid to a gentle simmer.

Preheat oven to 325°F (160°C). Cover the Dutch oven with a lid and transfer to the preheated oven. Braise for 2.5 to 3 hours, or until the short ribs are fork-tender and easily pull away from the bone.

Carefully remove the short ribs from the pot and set aside. Skim off any excess fat from the surface of the sauce. You can strain the sauce through a fine-mesh sieve for a smoother consistency, pressing on the solids to extract all flavor, or leave it chunky with the vegetables. Season the sauce with additional salt and pepper if needed.

Return the short ribs to the sauce and serve hot with your favorite sides.