Finely chop broccoli and saute in butter over medium heat in butter until broccoli is tender (but not mushy) and bright green. Add flour and stirr until all the butter is absorbed by the flour and saute for 2 minutes.
Stir in milk, half and half and salt and pepper. Slowly bring to a simmer stirring almost constantly over mediom heat, do not rush this step. once you have a decent simmer continue to cook and stir for 2 minutes.
Soup should be nicely thickened.
Serve with French bread.
This is the only recipe I learned from my maternal grandma before she died of breast cancer.
It is delicious, my kids ask for this one over and over.
Until I had this one I never liked cream of broccoli soup, but this one is so fresh and pure. It's not like most where the broccoli is over-cooked and has turned bitter.