In a 3-qt. saucepan, brown beef over medium-high heat; drain and set aside.
Melt 1 tablespoon of the butter in the saucepan. Add the onion, carrots, celery, basil, parsley, and garlic, then cook until the vegetables begin to soften.
Add the remaining butter. When melted, stir in the flour until the vegetables are coated.
Gradually add the chicken broth, stirring until smooth. Add the potatoes and bring the soup to a boil.
Reduce the heat, cover, and simmer until the potatoes are tender, about 10 to 12 minutes.
Return the beef to the saucepan. Stir in the cubed cheese, milk, salt, and pepper, and cook until the cheese melts.
Remove from the heat and stir in the sour cream. Serve warm.