To start, peel and chop up the potatoes and place them in a pot of bowling water. Now, boil them until fork tender. Remove them from the water then use a potato masher to mash them down until somewhat smooth. Set to the side.
In a large pot, brown the ground beef. Remove the browned ground beef then add in the onions and garlic. If the pan looks dry, add a little oil. Cook until they are soft and browning. When they are done, lower the pan to medium low heat and add in the butter.
Once the butter has melted, toss in the flour and cook the flour with the other ingredients for about 2 minutes. Next, add in the broth and milk while whisking. Then, add in the Worcestershire sauce, mixed veggies, browned ground beef, parsley and the mashed potatoes from earlier.
Stir everything together until the potatoes have mixed in with the milk and broth. Lower the heat then cover the pot and allow the soup to cook for 15-20 minutes. Come back occasionally and give it a stir. After the time is up, add salt and pepper to taste then serve with freshly grated parmesan cheese on top.