Season oxtails with salt, pepper, garlic, and minced thyme. You can do this step the night before and let it marinate overnight in the fridge for deeper flavor.
In a large cast iron pot or Dutch oven, heat the oil over medium-high heat. Sear the oxtails in the hot oil, turning to brown all sides. Remove and set aside.
Add the onion, carrot, and celery to the same pan and cook, stirring frequently, until the onions soften and brown slightly.
Stir in the garlic, thyme, bay leaves, and tomato paste and continue cooking for another minute or two.
Pour in the wine, stock, Worcestershire sauce, and beef bouillon powder. Lightly season with salt and pepper. Remember, you can add more salt if needed as you go, but you can't take it back out.
Return oxtails to the pot, bring to a boil, cover with the lid, and place it in the oven. Braise slowly for 2-3 hours, or until the oxtails are fork-tender. Check on them occasionally, adding stock as needed.
Remove from oven, garnish with parsley or green onions, and serve over rice, mashed potatoes, or another preferred side.