In a large pot, cook the ground beef over medium heat until browned and cooked through. Drain any excess grease.
Add the chopped onion, diced carrots, and diced celery to the pot. Cook until the vegetables are tender, about 5 minutes.
Stir in the diced potatoes, chicken broth, dried basil, and dried parsley. Bring to a boil, then reduce the heat and simmer until the potatoes are tender, about 10-15 minutes.
In a small bowl, whisk together the flour and milk until smooth. Gradually add the mixture to the soup, stirring constantly.
Cook the soup for another 5 minutes, or until it thickens slightly.
Stir in the shredded cheddar cheese until melted and well combined.
Remove the pot from the heat and stir in the sour cream. Season with salt and pepper to taste.
Serve the soup hot, garnished with extra shredded cheddar cheese and chopped fresh parsley if desired.