Buttery Onion Soup: revised

Neighbor Kay S. said she made this recipe last night and it was excellent so I decided to post it again.
I think I will be making this tonight after I go to the store for some mozzarella cheese.

Buttery Onion Soup 4/5/2008

2 Cups thinly sliced onions
1/2 Cup butter or margarine
1/4 Cup flour
2 Cups chicken broth
2 Cups milk
8 oz. shredded mozzarella cheese
salt and pepper to taste

Saute' onion in butter 20-30 minutes in 3 qt. sauce pan till nicely carmelized. Blend in
flour, add milk and broth, heat until boiling, boil one minute, reduce it
to low; remove from heat and let it cool down; the cool down process is important. Kay and I added the cheese on top of the bowl just before serving and this seemed to work well. Otherwise the cheese is stringy.