In a large pot, cook the ground beef over medium heat until browned. Drain and set aside.
In the same pot, add the onion, carrots, and celery. Cook until tender.
Add the chicken broth, potatoes, and cooked ground beef. Bring to a boil, then reduce heat and simmer until potatoes are tender.
In a small bowl, whisk together the flour and milk 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 until melted. Add the sour cream, salt, and pepper. Stir well and serve hot.