Heat the vegetable oil in a large pot over medium-high heat.

Sear the oxtail pieces until they are browned on all sides, then set aside.

In the same pot, add the chopped onion, carrots, and celery, and sauté until softened, about 5 minutes.

Add the minced garlic, bay leaves, and dried thyme to the vegetables.

Return the browned oxtail to the pot and pour in the beef broth and diced tomatoes.

Bring the soup to a boil, then reduce to a simmer and cover.

Simmer for about 2 to 3 hours until the oxtail is tender and falling off the bone.

Periodically skim off any fat that rises to the surface.

Once cooked, remove the oxtail, shred the meat from the bones, and return the meat to the soup.

Season with salt and pepper to taste and garnish with fresh parsley before serving.