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, pressing the seasoning into the meat.
03 - Heat olive oil in a large Dutch oven or heavy ovenproof pot over medium-high heat until shimmering. Add lamb shanks and sear on all sides until deeply browned, approximately 10 minutes total. Transfer browned shanks to a plate and set aside.
04 - Reduce heat to medium. Add onion, carrots, and celery to the pot. Sauté for 5 to 6 minutes until vegetables are softened and lightly colored. Add minced garlic and cook for 1 minute until fragrant.
05 - Stir in tomato paste and cook for 2 minutes to deepen flavor. Pour in red wine while stirring, scraping up any browned bits from the pot bottom. Bring to a simmer and cook until reduced by half, approximately 12 to 15 minutes.
06 - Return lamb shanks and any accumulated juices to the pot. Add stock, rosemary, thyme, and bay leaves. Bring liquid to a gentle simmer.
07 - Cover pot tightly with lid or aluminum foil. Transfer to preheated oven and braise for 2 to 2 1/2 hours. Turn shanks halfway through cooking. Meat is done when tender and easily pulls away from the bone.
08 - Remove lamb shanks from pot and tent loosely with foil to keep warm. Strain braising liquid through a fine-mesh sieve, pressing on solids to extract flavor. Skim excess fat from liquid surface. Return liquid to pot and simmer on stovetop over medium heat for 10 to 15 minutes until reduced to a silky, sauce-like 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.