Heat the vegetable oil in a large pot over medium heat. Add the lamb chunks and cook until browned on all sides.
Add the diced onion to the pot and cook until it softens.
Stir in the sliced carrots, parsnips, and cubed potatoes.
Add the pearl barley, broth, bay leaves, and thyme leaves. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for about 1 hour and 15 minutes until the lamb is tender and the barley is cooked.
Season with salt and black pepper to taste. Remove the bay leaves before serving.
Sprinkle the chopped parsley over each bowl.