Heat the olive oil in a large pot over medium heat. Add the lamb chunks and brown them on all sides for about 5 minutes. Season with salt and pepper.
Add the diced onion and minced garlic to the pot. Cook for 3 minutes until the onion softens.
Stir in the carrots, parsnips, and potatoes. Cook for another 3 minutes to start softening the vegetables.
Pour in the beef broth. Add the pearl barley, thyme sprigs, and bay leaf. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 60 minutes. Stir occasionally until the lamb is tender and the barley is cooked through.
Remove the thyme sprigs and bay leaf. Taste and adjust salt and pepper if needed. Sprinkle with chopped parsley before serving.