In a large pot over medium heat, brown the ground beef. Drain excess fat and set aside.
In the same pot, add diced onion, carrots, and potatoes. Sauté for about 5-7 minutes until onions are transparent.
Pour in the beef broth and bring to a boil. Reduce heat to low and simmer for 15 minutes or until the potatoes are tender.
Stir in the milk and let it heat through for about 5 minutes.
Gradually add the shredded cheddar cheese while stirring continuously until melted and creamy.
Taste and adjust seasoning with salt and pepper as needed.
Ladle the soup into bowls and serve hot. If desired, top with additional cheese or burger toppings like diced pickles or green onions.