Melt 1 tablespoon butter in a large pot over medium heat. Add onion, carrots, and celery; cook until soft. Add beef; cook until beef is brown.
Stir in basil and parsley. Add chicken broth and potatoes. Bring to a boil; then simmer until potatoes are tender; about 10-12 minutes.
In a medium saucepan, melt 3 tablespoons of butter and then whisk in flour. Add the milk and stir until smooth.
Gradually add the milk mixture to the soup, stirring constantly. Bring to a boil and reduce heat to a simmer. Stir in the cheese and stir constantly until melted. Add sour cream and heat through. Do not boil.