In a large pot, cook the ground beef over medium heat until browned. Drain and set aside.
In the same pot, add the onions, carrots, and celery. Cook until tender.
Add the potatoes and chicken broth. Bring to a boil, then reduce heat and simmer until potatoes are tender.
In a small bowl, whisk together the milk and flour until smooth. Gradually add to the soup, stirring constantly. Bring to a boil and cook until thickened.
Reduce heat to low. Stir in the cheese, sour cream, and cooked ground beef. Cook until cheese is melted and soup is heated through. Season with salt and pepper to taste.