Season Oxtails: Season the oxtails generously with salt and pepper.
Brown Oxtails: In a large pot or Dutch oven, heat the oil over medium-high heat. Add the oxtails in batches and brown on all sides. Remove and set aside.
Sauté Vegetables: In the same pot, add the onion and garlic, cooking until softened. Stir in the tomato paste and cook for another minute.
Cook Oxtails: Return the oxtails to the pot. Add beef broth, carrots, celery, thyme, and bay leaves. Bring to a boil, then reduce heat to low, cover, and simmer for 2-3 hours, or until the meat is tender.
Finish: Remove bay leaves and adjust seasoning with salt and pepper. Serve hot with Mac & Cheese.