Pat the lamb shanks dry and season them all over with salt and black pepper. Heat the olive oil in a large Dutch oven over medium-high heat, then brown the shanks on all sides. Remove them to a plate.
Add the onion, carrots, and garlic to the pot. Cook for 5 minutes until the onion softens.
Pour in the Guinness and scrape the bottom of the pot to loosen any browned bits. Let it bubble for 2 minutes.
Return the lamb shanks to the pot. Add the beef broth, potatoes, thyme, and bay leaves. Bring to a simmer, then cover and cook on low heat for 2 hours.
Stir in the shredded cabbage. Continue cooking uncovered for 30 minutes until the cabbage is tender and the lamb is very soft.
Remove the thyme sprigs and bay leaves. Taste and adjust salt and pepper if needed. Sprinkle with chopped parsley before serving.