01 - Heat a large skillet over medium heat. Add the lean ground beef and cook, breaking it apart with a spoon, until fully browned. Drain excess fat and set aside.
02 - Transfer the cooked beef to a 5-quart or larger slow cooker. Add the diced potatoes, onion, carrots, celery, and garlic.
03 - Sprinkle the flour, thyme, parsley, paprika, salt, and pepper over the ingredients. Stir thoroughly to distribute the seasonings evenly.
04 - Pour in the beef broth. Cover and cook on LOW for 6 hours or HIGH for 3-4 hours, until potatoes and vegetables are fork-tender.
05 - In a small bowl, whisk together the whole milk and softened cream cheese until completely smooth.
06 - Pour the milk mixture into the slow cooker. Add the heavy cream and shredded cheddar cheese. Stir well to incorporate.
07 - Cover and continue cooking on HIGH for 20-30 minutes, stirring occasionally, until the soup is thickened and the cheese is fully melted.
08 - Taste the soup and adjust salt or pepper if needed. Serve hot, garnished with chopped fresh chives, extra cheddar cheese, or crumbled bacon if desired.