Cook the ground beef in a large dutch oven or large pot. Pour the beef into a strainer to drain out all the excess grease and set the meat aside. Using the same pot, melt butter and saute the onion, celery and carrots until tender. Add in the Worcestershire sauce and garlic.
Stir in the flour to coat the vegetables, this will help thicken the soup while it cooks. Pour in the broth and using a wooden spoon gently scrape the bottom of the pot to get all the flavored bits off the bottom.
Add in the seasonings. Stir to combine. Add in the diced potatoes and ground beef. Simmer until potatoes are softened, about 15-20 minutes. Remove from heat and stir in milk and cheese.