In a large skillet over medium-high heat, cook the ground beef until browned, breaking it apart with a spoon. The beef is done when it reaches an internal temperature of 160°F (71°C). Drain off any excess fat and transfer the cooked beef to a 6-quart or larger slow cooker.
Add the chopped onion, shredded carrots, diced celery, minced garlic, dried basil, dried parsley, diced potatoes, and chicken broth to the slow cooker. Stir to combine.
Cover the slow cooker and cook on LOW for 6-8 hours or on HIGH for 3-4 hours, until the potatoes are tender when pierced with a fork.
About 30 minutes before serving, prepare the cheese sauce. In a small saucepan over medium heat, melt the butter. Whisk in the flour and cook for 1 minute, stirring constantly.
Gradually whisk the milk into the saucepan. Continue to cook, whisking frequently, until the sauce thickens and begins to bubble, about 3-5 minutes.
Remove the saucepan from the heat and stir in the softened cream cheese until it has melted completely into the sauce.
Pour the creamy milk mixture into the slow cooker. Stir well to combine with the soup base.
Add the shredded cheddar cheese to the slow cooker in handfuls, stirring after each addition until the cheese is fully melted and the soup is smooth.
Taste the soup and season with salt and pepper as needed. Serve hot.