Heat a large pan over medium-high heat. Add oil and let heat 1 minute.
Brown meat in batches (allowing space around each piece) medium-high heat. Remove from pan and place in a 4-6 quart slow cooker.
Add onions to the saute pan and cook over medium heat until translucent -- they will pick up all the brown bits left by the meat! Stir in garlic, salt, Italian seasoning and pepper and cook 1 minute.
Add the onions to the slow cooker on top of the beef, along with the carrots, celery, barley, tomato paste and bay leaves. Stir well, and then stir in the beef broth.
Cover and cook on low for 6-8 hours, or on high for 3-4 hours, until vegetables and barley are tender.
Stir in fresh parsley as desired and season to taste. Serve.