Cut vegetables into small pieces, discarding any of the stem too tough to poke with a fingernail. Barely cover with broth and slowly cook until tender. In another pan, saut onion in butter or margarine on medium heat.
Add flour to make a roux; slowly add flour, stirring constantly to thicken and prevent lumping. Slowly add milk while stirring constantly. Lower heat and cook 45 minutes; continue stirring occasionally. Serve with grated cheese and pepper.