Heat the vegetable oil in a large Dutch oven over medium heat. Add the lamb chunks and brown them on all sides, then remove and set aside.
Add the chopped onion and sliced carrots to the pot. Cook for a few minutes until the onion softens.
Return the lamb to the pot. Pour in the broth and add the bay leaves and thyme. Bring to a simmer, then cover and cook for 45 minutes.
Add the quartered potatoes to the pot. Continue simmering for 20 minutes.
Place the cabbage wedges on top of the stew. Cover and cook for another 15 minutes until the cabbage is tender but still holds its shape.
Remove the bay leaves. Season with salt and pepper to taste, then sprinkle with the chopped parsley before serving.