1. Heat the oil in a 4-quart stock pot or saucepan over medium-high heat. Add the onions and garlic and cook over medium heat until the onions begin to caramelize, about 10 minutes. Add the celery and carrots; cook until vegetables soften, about 5 minutes. Push the vegetables to one side of the pot, add the beef, and brown both sides 3 to 5 minutes.
2. Add the water, ½ cup parsley, salt, and pepper. Bring to a boil over high heat, reduce to low, cover, and simmer until the beef is tender, at least 1 hour. Remove the beef and let cool. Remove the meat from the bone and the marrow from inside the bone, chop into bite-size pieces, and return to the pot along with the barley.
3. Cook, covered, for 45 minutes or until barley is tender. Taste and adjust seasoning. Serve sprinkled with the remaining parsley.