Brown the Beef: In a large pot, cook the ground beef over medium heat until browned. Drain any excess fat.
Sauté Vegetables: Add chopped onion and minced garlic to the pot with the beef. Sauté until the onion is translucent.
Add Potatoes and Broth: Stir in diced potatoes, and pour in the beef broth. Bring the mixture to a boil, then reduce heat and simmer until potatoes are tender.
Incorporate Remaining Ingredients: Add milk, shredded cheese, corn, peas, carrots, thyme, and rosemary. Cook on low heat until the cheese is melted and vegetables are cooked through.
Season and Serve: Season the soup with salt and pepper to taste. Serve hot, garnished with chopped parsley if desired.