In a large pot, cook the ground beef over medium heat until no longer pink. Drain and set aside.
In the same pot, add the onions, carrots, and potatoes. Cook until tender.
Stir in the chicken broth and bring to a boil. Reduce heat, cover, 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, sour cream, and cooked ground beef. Cook and stir until cheese is melted and soup is heated through. Season with salt and pepper to taste.