Step 1: Pat the short ribs dry with paper towels and season generously with salt and black pepper.
Step 2: Heat olive oil in a large Dutch oven or oven-safe pot over medium-high heat. Sear the short ribs on all sides until deeply browned, about 3-4 minutes per side. Remove ribs and set aside.
Step 3: Add chopped onion, carrots, and celery to the pot. Sauté until softened, about 5-7 minutes. Add minced garlic and tomato paste, cooking for another 2 minutes until fragrant.
Step 4: Pour in the red wine, scraping up any browned bits from the bottom of the pot. Bring to a simmer and reduce by about half, approximately 10-15 minutes.
Step 5: Stir in the beef broth, rosemary, thyme, and bay leaves. Return the seared short ribs to the pot, ensuring they are mostly submerged in the liquid. Bring back to a gentle simmer.
Step 6: Cover the Dutch oven and transfer to a preheated oven at 325°F (160°C). Braise for 2.5 to 3 hours, or until the short ribs are fork-tender and practically falling off the bone.
Step 7: Carefully remove the short ribs from the pot and set aside on a plate, covered loosely with foil. Discard rosemary, thyme stems, and bay leaves from the sauce.
Step 8: If desired, skim off any excess fat from the sauce. For a thicker sauce, you can reduce it further on the stovetop over medium-high heat until it reaches your desired consistency. Taste and adjust seasoning.
Step 9: Serve the tender short ribs with the rich red wine sauce, alongside your favorite sides like mashed potatoes or polenta.