In a large saucepan, brown the ground beef, drain it, then set aside. In your soup pot, melt 1 tablespoon of butter and saute your onion, carrots, celery, basil, and parsley for around 10 minutes, or until the onions are translucent. Now add the ground beef, chicken broth, and potatoes and bring the soup to a boil. Once it begins to boil, reduce the heat, cover, and simmer for around 10 minutes. After 10 minutes, check to see if your potatoes are cooked. If not, simmer for a bit longer.
In a small skillet melt the remaining 3 tablespoons of butter. Add the flour to the butter and cook over a medium to high heat, until it gets bubbly and a bit thick. Slowly add this mixture to the soup, and bring the soup back to a boil. Once it’s boiling, cook for around 2 minutes. The soup should start to thicken.
Reduce your heat to low and add the cheese, milk, salt and pepper. Continue to cook over a low heat until all the cheese has melted. The smaller you made the cubes of of cheese, the faster this will happen.
Remove the soup from the heat, ans stir in the sour cream. Enjoy!