Place potatoes, diced onion, celery, carrots, basil, parsley, and chicken broth in a slow cooker. Cook on low 7-8 hours or on high 3-4 hours.
About 30 minutes before serving, add oil and ground beef to a large sauce pan and stir over medium heat for 4-5 minutes until browned. Transfer to a bowl and wipe out the pan with a paper towel.
Add butter to pan and stir until melted. Add flour and stir until mixture clumps up. Slowly whisk in milk (half and half OR heavy cream) until mixture thickens. Stir in salt, pepper, and sour cream.
Add cream mixture, ground beef, and shredded cheese to crock pot. Stir to combine all ingredients. Serve warm and top with additional cheese, bacon bits, and green onions if desired.