Brown the ground beef, making sure to breaking up the chunks well. Drain and set aside/
In a medium kettle, sauté the onion, carrot, celery, basil, and parsley in 1 tbsp of the butter until the veggies are softened but leave a little crunch on them.
Add the broth, potatoes, and meat into the kettle, bringing it to a boil. Reduce heat and simmer until the potatoes begin to soften.
Make a small rue by melting the remaining butter in a small pan. One melted add the flour and whisk well until, cooking it for about 2 minutes. You can cook it a little longer if you like a darker rue and a deeper flavor. Add this to the kettle when done.
Bring the kettle to a boil again and cook for 2 minutes to allow the rue to incorporate and begin to thicken the soup.
Reduce heat to LOW and add the cheese, milk, and Salt/Pepper. You want the cheese to fully melt but do not overheat this.
Remove from the heat and add the sour cream, mixing it well. Serve right away but it's also great the next day.
Option: If you want to remove the potatoes you can substitute them for macaroni pasta, just put the pasta in the bowl and server the soup over the top of it.
Option: My kids are not big celery fans and we've tried to leave it out, it's not as good. Instead I would suggest you leave it in but leave it cut larger for easy picking out.
Reheating: You may need to add a teaspoon or two of milk if the soup gets too thick.