01 - Set the oven to 320°F (160°C) to prepare for braising.
02 - Generously season the lamb shanks with salt and freshly ground black pepper.
03 - Heat olive oil in a large ovenproof pot over medium-high heat. Brown the lamb shanks on all sides, about 8 minutes total, then remove and set aside.
04 - Add onions, carrots, and celery to the pot. Cook for 5–6 minutes until softened, then add garlic and sauté for 1 more minute.
05 - Stir in tomato paste, then pour in the red wine. Simmer for 3–4 minutes, scraping up browned bits from the pot bottom.
06 - Return lamb shanks to the pot. Add chopped tomatoes, stock, bay leaves, thyme, rosemary, and smoked paprika. Stir well and bring to a simmer.
07 - Cover with a tight-fitting lid and transfer to the oven. Cook for 2½ to 3 hours, turning the shanks halfway through, until meat is tender and falling from the bone.
08 - Skim excess fat from the surface, then adjust seasoning with salt and pepper as needed.
09 - Plate the lamb shanks, spooning generous amounts of sauce over each. Serve hot with creamy mashed potatoes or polenta.