Sear the oxtails Heat vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the oxtails in batches until browned on all sides. Remove and set aside.
Sauté the vegetables In the same pot, add onion, carrots, and celery. Cook for about 5 minutes until softened and lightly caramelized. Add garlic and cook for 1–2 minutes until fragrant.
Build the base Stir in the tomato paste and cook for 2 minutes to deepen its flavor.
Deglaze with wine Pour in the red wine, scraping up browned bits from the bottom. Let it simmer and reduce by half (about 5 minutes).
Braise the oxtails Return the oxtails to the pot. Add beef broth, ensuring the meat is mostly covered. Add thyme and bay leaves. Bring to a simmer, then cover and cook on low heat for 3–4 hours, until tender.
Finish the sauce Remove oxtails and discard thyme and bay leaves. Blend the sauce until smooth (optional). Simmer uncovered if needed to thicken.
Final step Season to taste. Return oxtails to the sauce and simmer for 10 minutes to coat and reheat.
