Heat the oil in a large Dutch oven over medium-high heat. Add the lamb neck pieces and brown them on all sides, about 8 minutes total. Remove the lamb and set it aside.
Add the onion to the pot and cook until softened, about 5 minutes. Stir in the garlic and cook for 1 minute more.
Pour in the Guinness and scrape up any browned bits from the bottom. Return the lamb to the pot along with the beef broth, thyme, salt, and pepper. Bring the mixture to a simmer, then cover and cook on low heat for 1 hour and 30 minutes.
Add the potatoes and continue cooking for 30 minutes. Stir in the cabbage and cook for another 15 minutes until the cabbage is tender and the lamb pulls easily from the bone.