01 - Preheat the oven to 320°F.
02 - Generously season the lamb shanks with salt and freshly ground black pepper.
03 - Heat olive oil in a large ovenproof pot or Dutch oven over medium-high heat. Sear the lamb shanks on all sides until browned, about 8 minutes. Remove and set aside.
04 - Add onions, carrots, and celery to the pot and sauté for 5 to 6 minutes until softened. Add garlic and cook for an additional minute.
05 - Stir in the tomato paste, then pour in the red wine. Simmer for 3 to 4 minutes, scraping the pot to release browned bits.
06 - Return lamb shanks to the pot. Add chopped tomatoes, stock, bay leaves, thyme, rosemary, and smoked paprika. Stir to combine and bring to a simmer.
07 - Cover with a tight-fitting lid and transfer to the oven. Cook for 2.5 to 3 hours, turning the shanks halfway through, until meat is tender and falling off the bone.
08 - Skim any excess fat from the surface. Adjust seasoning with salt and pepper as needed.
09 - Serve hot, spooning plenty of the rich sauce over each lamb shank. Pair well with creamy mashed potatoes or polenta.