In a large pot over medium heat, brown the ground beef until fully cooked. Drain excess fat.
Add the diced onion and minced garlic to the pot, cooking until the onion is translucent, about 3-4 minutes.
Stir in the beef broth, diced potatoes, carrots, celery, Worcestershire sauce, mustard, salt, and black pepper. Bring to a boil, then reduce heat and let simmer for 15-20 minutes, or until the vegetables are tender.
Stir in the shredded cheddar cheese and milk, mixing until the cheese is melted and the soup is creamy.
Add the cornstarch mixture to the soup, stirring continuously until the soup thickens, about 2-3 minutes.
Serve hot, garnished with chopped green onions if desired.