Season oxtails generously with salt and black pepper.
Heat vegetable oil in a large, heavy-bottomed pot over medium-high heat. Sear oxtails until browned on all sides. Remove and set aside.
In the same pot, add onions, celery, and carrots. Cook for 5–7 minutes until vegetables are softened.
Stir in minced garlic and tomato paste. Cook for 2 more minutes.
Return oxtails to the pot. Pour in beef broth and red wine (if using). Add Worcestershire sauce, thyme, and bay leaves.
Bring to a boil, then reduce heat to low. Cover and simmer for 3 hours, or until meat is fork-tender.
Remove bay leaves before serving. Serve hot over mashed potatoes or rice.