In a 3-quart saucepan or Dutch oven, brown the ground beef over medium high heat, breaking into small pieces as it cooks. When cooked through, drain excess fat, transfer meat to a plate, and set aside.
In the now-empty pan, melt the butter over medium heat. Add the garlic, onion, celery, carrots, and Worcestershire. Cook, stirring frequently, until onions become translucent, about 2-3 minutes. Add flour and cook, while whisking, for about 1 minute. Gradually add in the chicken broth and milk, and cook, while whisking, for 1-2 minutes. Stir in the potatoes and bring to a boil.
Reduce heat and simmer until potatoes are tender, about 12-15 minutes. Stir in ground beef, cheese, salt, and pepper. Stir until cheese is melted. If the soup is too thick, add a little more milk.
Serve garnished with crumbled bacon, shredded cheddar cheese, green onions, diced fresh tomato, or whatever your heart desires.