01 - Preheat the oven to 320°F.
02 - Season lamb shanks generously with salt and freshly ground black pepper.
03 - Heat olive oil in a large ovenproof pot or Dutch oven over medium-high heat. Brown lamb shanks on all sides, about 8 minutes. Remove and set aside.
04 - Add onions, carrots, and celery to the pot; sauté for 5 to 6 minutes until softened. Add garlic and cook for 1 additional minute.
05 - Stir in tomato paste, then pour in red wine. Simmer for 3 to 4 minutes, scraping up browned bits from the pot.
06 - Return lamb shanks to the pot. Add chopped tomatoes, beef or lamb stock, bay leaves, thyme, rosemary, and smoked paprika. Stir to combine and bring to a simmer.
07 - Cover the pot with a tight-fitting lid and transfer to the oven. Cook for 2½ to 3 hours, turning lamb shanks halfway through, until meat is tender and falling off the bone.
08 - Skim excess fat from the surface. Adjust seasoning with salt and pepper to taste.
09 - Serve lamb shanks hot with ample sauce spooned over each piece. Ideal with creamy mashed potatoes or polenta.