Heat a heavy-bottomed saucepan to medium heat. Add 3 tbsp of vegetable oil, then add celery, carrots and onion. Sauté for 3 minutes, then add garlic. Continue cooking until onions become translucent, about 5 minutes.
Add the red wine and bring to high heat. Cook until the alcohol has burned off. Add the beef stock and then add the oxtails. Adjust the heat to bring the liquid down to a low simmer. Add bay leaves and thyme.
Bring to a low simmer and add bay leaf and thyme. Cover and cook for 2 hours, or until meat is a bit tender. Add potatoes and cook an additional 30 minutes, or until potatoes are cooked through. Add salt and pepper to taste.