Preheat the oven to 325°Fahrehheit.
Remove the ribs and pat dry with a paper towel. Season generously with salt and black pepper.
Set a large oven-safe pot or Dutch oven over medium-high heat. Add the oil and swirl to coat the entire surface of the pan. Working in batches, sear the short ribs for approximately one minute per side, being careful not to overcrowd the pan.
Remove the seared ribs from the pan and set aside. Repeat until all of the short ribs have been seared.
Return the same oven-safe pot or Dutch oven to medium heat. Add the carrots, celery, onion, garlic, tomato paste, salt and black pepper, mixing well to combine. Cook for 5-8 minutes, or until the vegetables have softened slightly.
Pour in the beef broth and red wine. Bring to a simmer over medium heat. Simmer for about 5 minutes (reducing heat if necessary to prevent rapid boiling).
Return the seared short ribs to the pot with the vegetables and broth. Add the fresh thyme and bay leaves.
Cover the pot with a lid - slightly tilting the lid to allow a little ventilation - then transfer it to the preheated oven.
Braise the ribs for 3-4 hours, or until the meat is tender and falling off the bone.
Remove the pot from the oven and carefully remove the ribs to a clean plate. Strain the broth into a bowl and refrigerate for at least 2-3 hours, separating the fat from the beef broth. Once the fat has hardened and separated, remove the fat and discard (optional).
Reheat the broth in a pan on low heat and simmer until it has thickened then add the ribs back to the sauce and cook for an additional 5 minutes.
Serve over yummy mashed potatoes or creamy polenta.