Pat the oxtail pieces dry with paper towels and season generously with salt, pepper, and a dusting of flour to coat them lightly.

Heat the olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat, then sear the oxtail pieces on all sides until deeply browned, about 8-10 minutes.

Remove the oxtail from the pot and set aside, then add the chopped onion, carrots, and celery to the same pot, sautéing until the onions are translucent and fragrant, about 5 minutes.

Stir in the minced garlic and tomato paste, cooking for another minute until the paste darkens slightly, then pour in the red wine to deglaze the pot, scraping up any browned bits from the bottom.

Return the oxtail pieces to the pot and pour in the beef broth and dried thyme, ensuring the meat is mostly submerged in the liquid.

Bring the mixture to a boil, then reduce the heat to low, cover with a lid, and let it simmer gently for 2.5 to 3 hours, or until the meat is very tender and pulling away from the bone.

About 20 minutes before serving, stir in the broad beans (remove skins if using fresh mature beans) and simmer uncovered to allow the sauce to thicken slightly and the beans to cook through.

Taste the stew and adjust seasoning with additional salt and pepper if needed, then skim off any excess fat from the surface before serving.

Serve hot in shallow bowls, garnished with fresh parsley if desired, alongside mashed potatoes or crusty bread to soak up the rich gravy.