01 - Preheat the oven to 325°F.
02 - Pat lamb shanks thoroughly dry with paper towels. Season generously on all sides with salt and pepper.
03 - Heat olive oil in a large Dutch oven or heavy ovenproof pot over medium-high heat. Sear lamb shanks on all sides until deeply browned, approximately 10 minutes total. Transfer browned shanks to a plate and set aside.
04 - Add onion, carrots, and celery to the remaining fat in the pot. Sauté for 5 to 6 minutes until vegetables are softened and lightly golden. Add minced garlic and cook for 1 minute until fragrant.
05 - Stir in tomato paste and cook for 2 minutes to caramelize. Pour in red wine, using a wooden spoon to scrape up any browned bits from the bottom of the pot. Bring to a simmer and reduce by half, approximately 12 to 15 minutes.
06 - Return lamb shanks to the pot. Add stock, rosemary, thyme, and bay leaves. Bring to a gentle simmer, then cover tightly with the lid.
07 - Transfer the covered pot to the preheated oven. Braise for 2 to 2½ hours, turning shanks halfway through cooking, until meat is fork-tender and nearly falling from the bone.
08 - Remove shanks from the pot and cover loosely with foil to keep warm. Strain the braising liquid through a fine-mesh sieve, discarding solids. Skim excess fat from the surface. Simmer the strained liquid on the stovetop over medium heat for 10 to 15 minutes until reduced to a silky, coating consistency.
09 - Return lamb shanks to the reduced sauce and warm through for 2 to 3 minutes. Serve immediately, garnished with fresh chopped parsley if desired.