Preheat your oven to 160°C/325°F. Season the beef short ribs generously with salt and pepper on all sides. Heat the olive oil in a large, oven-safe pot over high heat. Sear half of the ribs until they are deeply browned all over, which should take about 5 to 7 minutes in total. Remove these ribs and repeat the process with the remaining ribs, then set them aside.
Reduce the heat to medium and add the chopped onion and crushed garlic to the same pot. Cook for about 2 minutes until they begin to soften. Incorporate the chopped carrots and celery, cooking for an additional 5 minutes until the carrots start to soften and release their sweetness.
Mix in the tomato paste and cook for another minute to allow the flavors to meld. Pour in the dry red wine and beef broth, adding the thyme sprigs and bay leaves. Stir the mixture thoroughly until the tomato paste is fully dissolved.
Place the seared ribs back into the pot, ensuring they are submerged in the liquid (Note 3). Cover the pot with a lid and transfer it to the preheated oven. Let it cook for approximately 3 hours or until the meat is so tender that it can be easily pulled apart with a fork (Note 4 for other cooking methods).
Carefully remove the ribs from the pot, keeping the meat intact on the bone. Cover them to keep warm. Strain the liquid from the pot, pressing down on the vegetables to extract all the juices. This step can be skipped if you prefer a chunkier sauce. Return the strained sauce to the pot, bring it to a simmer, and adjust the consistency as needed—reduce to thicken or add water to thin. Season with additional salt and pepper if required.
Arrange the ribs on a serving plate and generously spoon the sauce over them. Serve immediately and enjoy!