01 - Preheat oven to 320°F or set slow cooker to low setting
02 - Pat lamb shanks dry with paper towels and season generously with salt and black pepper on all sides
03 - Heat olive oil in a large Dutch oven over medium-high heat. Sear lamb shanks on all sides until deeply browned, approximately 8 minutes total. Transfer to a plate and set aside
04 - In the same pot, add onions, carrots, and celery. Cook for 5 to 7 minutes until softened, stirring occasionally. Add minced garlic and cook for 1 minute more
05 - Stir in tomato paste and cook for 1 minute. Pour in red wine while scraping up any browned bits from the pot bottom. Simmer for 2 to 3 minutes
06 - Add beef stock, rosemary sprigs, thyme, and bay leaves to the pot. Return lamb shanks to the pot, nestling them into the vegetables. Bring to a gentle simmer
07 - Cover pot and transfer to preheated oven. Braise for 3 to 3.5 hours, until meat is very tender and nearly falling from the bone. Alternatively, place all ingredients in slow cooker and cook on low for 8 hours
08 - Remove lamb shanks to a warm platter and tent loosely with aluminum foil. Discard bay leaves and rosemary stems from the braising liquid
09 - Skim excess fat from the surface of the sauce. For a thicker gravy, mix cornstarch with 2 tablespoons cold water until smooth, then whisk into simmering sauce until thickened to desired consistency
10 - Taste sauce and adjust seasoning with salt and pepper as needed. Serve lamb shanks with generous amounts of rosemary gravy spooned over the top