Place potatoes, onions, carrots, celery, dried basil and parsley in a large crock pot. Pour chicken broth over vegetables. Cover with lid. Cook on low heat 4 - 5 hours or until potatoes are tender.
About 45 minutes before serving, cook and crumble ground beef in a skillet over med-high heat. Drain fat. Pour cooked beef into crock pot. Wipe out hot skillet with a paper towel then add the butter. When the butter is melted whisk in flour and cook until golden brown and bubbly (about one minute). Whisk in the milk, salt and pepper and pour mixture into the crock pot and stir to combine.
Add the cubed Velveeta or shredded cheese to crock pot and stir again. Cover and cook another 30 minutes or until cheese is melted.