Heat a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the seasoned lamb chops in the hot pot on both sides until browned
Add the chopped onion, minced garlic, and 1 bay leaf to the pot. Saute a few minutes until soft.
Add just enough water to the pot to fully cover the lamb chops. Bring the liquid to a boil, then immediately reduce the heat to a low simmer
Cover the pot and allow the meat to cook for 1.5 hours (90 minutes). You may keep the pot simmering on the stovetop or transfer it to a preheated 325 oven for this stage
After the lamb has cooked for 1.5 hours, add the chopped potatoes and carrots to the pot. Season the vegetables with salt and pepper.
Cover and let the dish simmer for another 30 minutes. Ensure there is still enough liquid (now a rich broth) in the pan; if not, add a little more water, but aim for the water to have reduced down.
Carefully remove the lamb bones from the pot. The meat will be extremely tender and fall off the bone. Break up the meat with a spoon to ensure all small bones are collected and removed
Add the cabbage and cook another 15 minutes, or until the cabbage is tender.
Serve with a pat of butter and a sprinkle of grated Irish cheddar and some chopped parsley.