Season the oxtails generously with salt and black pepper.
Heat olive oil in a large pot or Dutch oven over medium-high heat.
Brown the oxtails on all sides, then remove them from the pot and set aside.
In the same pot, add the onions, carrots, and celery.
Cook until softened, about 5–7 minutes.
Add the garlic and tomato paste, stirring for 1–2 minutes until fragrant.
If using wine, pour it into the pot to deglaze, scraping up the browned bits from the bottom.
Let the wine simmer until it reduces by half.
Return the oxtails to the pot.
Add the beef broth, thyme, rosemary, bay leaves, Worcestershire sauce, and smoked paprika.
Bring everything to a boil, then reduce the heat to low.
Cover the pot and let the oxtails simmer for 2½ to 3 hours, or until the meat is tender and falling off the bone.
Stir occasionally and add more broth if needed.
Remove the herbs and bay leaves.
Skim any excess fat from the surface.
Adjust seasoning with additional salt or pepper if needed.
Garnish with fresh parsley or chives before serving.
Serve the braised oxtails over:
Creamy mashed potatoes
Steamed rice
Soft polenta
Add a side of sautéed greens or roasted vegetables for a complete meal.