01 - Set the oven to 320°F (160°C).
02 - Generously season the lamb shanks with salt and black pepper.
03 - Heat olive oil in a large, heavy-based ovenproof pot over medium-high heat and brown the lamb shanks on all sides, about 8 minutes. Remove and set aside.
04 - Add onions, carrots, and celery to the pot and cook for 5 to 6 minutes until softened. Stir in garlic and cook for 1 additional minute.
05 - Mix in tomato paste, then pour in the red wine. Simmer for 3 to 4 minutes, scraping up browned bits from the pot base.
06 - Return lamb shanks to the pot. Add chopped tomatoes, beef stock, bay leaves, thyme, rosemary, and smoked paprika. Stir thoroughly and bring to a simmer.
07 - Cover the pot tightly and place it in the oven. Cook for 2½ to 3 hours, turning the shanks halfway through cooking, until meat is tender and falling off the bone.
08 - Remove excess fat from the surface and adjust seasoning with salt and pepper to taste.
09 - Serve immediately, spooning generous amounts of sauce over each shank. Ideal with creamy mashed potatoes or polenta.