Add potatoes, diced onion, celery, carrots, basil, parsley, and chicken broth into a slow cooker. Cook on LOW for 7 to 8 hours --or-- on HIGH for 3 to 4 hours.
30 minutes prior to serving, heat oil in a skillet over medium heat. Add ground beef and crumble while it browns. Set aside.
Wipe the skillet with a paper towel and then add butter to the skillet and stir until it melts.
Add flour and stir until it soaks up the butter. Slowly, whisk in half and half or heavy cream until the mixture is smooth and thickens.
Add salt, pepper, and sour cream to the skillet.
Add cream mixture from skillet, ground beef, and shredded cheese to the crockpot and stir to combine.
Serve warm with additional cheese, bacon bits, green onions, and diced tomatoes on top, if desired.