Brown Beef: Heat oil in a pot over medium-high heat. Brown beef in batches if needed. Remove and set aside.
Cook Onions: Add onions to the pot and cook until softened (3 minutes).
Simmer: Return beef to the pot. Add broth, tomatoes, bay leaves, salt, and pepper. Bring to a boil, then reduce heat and simmer, covered, until beef is tender (55-75 minutes).
Add Vegetables: Stir in potatoes, carrots, and celery. Cook for 20 minutes. Then add green beans and green onions. Simmer for 10 more minutes.
Finish: Stir in parsley, adjust seasoning if needed, and remove from heat.
Enjoy your hearty, comforting soup!