Place ground beef in a skillet over medium heat. Cook, breaking into pieces, until browned and cooked through. Drain.
Place beef in a crockpot along with the onion, carrots, celery, potatoes, basil, parsley, salt, and broth. Cook on low for 4 hours or on high for 2 hours.
Whisk together the flour and milk. Add to the crockpot, along with the butter and shredded cheese. Cook for an additional 1 hour on high.
Transfer soup to bowls and garnish with sour cream and chives.
Notes
You can use 80%, 85%, or 90% lean beef for this recipe. I highly recommend shredding the cheese yourself. Pre-shredded cheese contains potato starch, which can prevent it from melting nicely into the soup.