Add carrots, celery, potatoes, diced tomatoes, and tomato paste to the pot. Stir well to combine and coat vegetables with the tomato base.
Step 4: Build the Soup
Return the browned beef to the pot. Pour in the beef broth and add salt, pepper, basil, oregano, and bay leaf. Stir to combine.
Step 5: Simmer Until Tender
Bring the soup to a boil, then reduce heat to low. Cover and simmer for 45–60 minutes, stirring occasionally, until the beef is tender and vegetables are cooked through. Add green beans and corn during the last 15 minutes of cooking.