In giant pot: brown beef, drain, set aside.
In same pot: saute carrots and basil in 2-tbsp butter until tender (~10 minutes)
Add broth, potatoes, and beef; bring to boil.
Reduce heat; cover and simmer for 15-20 minutes (or until potatoes are tender).
Meanwhile, make the roux: in small saucepan, melt 6-tbsp butter, add flour, cook and stir for 2-3 minutes. Time this so it's ready when the above is done.
Add the roux to the soup, bring to boil, cook and stir for 2 minutes.
Reduce heat to low.
Add cheese, milk, salt, and pepper; cook and stir until cheese melts. Throw some red pepper in there.
Remove from heat, blend in sour cream.
Yields 4.5 quarts.