Heat avocado oil in a heavy pot over medium-high heat. Sear oxtails in batches, about 3–4 minutes per side, until deeply browned. Remove and set aside.
Add onion and celery to the pot, cooking 6–7 minutes until softened. Add garlic and cook 1 minute more.
Stir in tomatoes, broth, bay leaves, thyme, and smoked paprika.
Return oxtails to the pot, cover, and simmer 2 to 2 1/2 hours, until meat is falling off the bone.
Remove bay leaves, season with salt and pepper, and serve with the rich braising liquid spooned over top.