Brown the ground beef in a large pot over medium heat for 5-7 minutes, breaking it apart. Drain excess fat.
Sauté diced onion and minced garlic for 3-4 minutes until translucent. Add diced potatoes, carrots, and celery, stirring to soften.
Pour in beef broth and add dried basil, oregano, salt, and pepper. Bring to a boil, then reduce heat and simmer for 15-20 minutes.
Whisk together milk and flour until smooth. Add to the pot, stirring constantly. Then add Worcestershire sauce and cheddar cheese, stirring until melted.
Taste and adjust seasoning. Simmer for a few more minutes, then serve garnished with chopped green onions.