Cheeseburger Soup

"A good hearty soup", a friend of mine said, and that it is.

1 pound hamburger scrambled slightly crispy [set aside and in the same pot saute the following with 1T butter and some oil if needed:
1 white or yellow onion chopped
6 carrots shredded
3 stalks celery chopped
1.5t each parsley, basil, thyme, rosemary
Add the following to the above mixture:
4C beef broth
hamburger
4 medium to large potatoes diced
1t salt (I like to salt as I go, so everything has maximum flavor.)
1t pepper
In another small pot melt 3T butter and whisk in 1/4C flour, cook for 1 minute whisking, adding broth if needed. Add to soup when potatoes are tender. Bring soup to a boil stirring constantly while it thickens.
Add the following to the soup:
1C milk, cream or half and half, depending on how rich you like it.
2 cheddar cheese shredded
Salt to taste if needed.