Brown and crumble ground beef. Drain excess grease and set aside.
Melt butter in a large stockpot or Dutch oven over medium heat. Add garlic, onion, carrots and Worcestershire. Cook, stirring frequently, until onions have become translucent, about 2-3 minutes.
Gradually pour in beef broth, Add the potatoes. Bring to a boil; reduce heat and simmer until potatoes are tender, about 12-15 minutes. You can add a little water or more broth if needed to keep the potatoes covered in liquid while cooking.
When the potatoes are tender, stir in the milk and bring soup back to a simmer. Then, add in the cooked ground beef, cheese, salt and pepper, to taste. Stir until cheese is melted and mixture is creamy and bubbling.
If the soup is too thick, add more milk as needed until desired consistency is reached.
Don't forget the toppings! They are what make this soup taste like a cheeseburger.