In a large skillet, cook beef and onion over medium heat until meat is no longer pink; drain. Combine flour and 1 can broth until smooth. Add to beef mixture. Bring to a boil; cook and stir until thickened, about 2 minutes.
Transfer to a 5-qt. slow cooker. Stir in the potatoes, carrots, celery, seasonings and remaining broth. Cover and cook on low for 6-8 hours or until vegetables are tender.
Stir in cheese and milk. Cover and cook until cheese is melted, about 30 minutes longer. Just before serving, stir in sour cream.