Dust the oxtails in flour, shaking off excess.
Heat oil over medium, then brown oxtails in batches; set aside.
Lower heat, add celery and onion, cooking for 2–3 minutes.
Add garlic, pepper, tomato paste, allspice berries, and cook 2–3 more minutes.
Preheat the oven to 375°F (190°C).
Return oxtails to pot, add salt, pour in wine, and scrape up browned bits.
Add beef stock to nearly cover meat. Stir in green seasoning, carrots, bay leaves, and brown sugar. Bring to a gentle boil.
Cover pot slightly ajar and transfer to preheated oven. Braise for 2 1/2–3 hours, checking every 15–20 minutes and adding stock if needed.
Remove bay leaves, stir in parsley, skim fat, and adjust salt. Serve hot with garlic mashed cassava or rice.