In a medium sauce pan, melt butter over medium-high heat. Add onion and saute 5 minutes or until onion is tender. Sprinkle with flour; cook 1 minute, stirring onion mixture constantly.
Add potato, broccoli, milk, broth and water to pan; bring to boil. Cover, reduce heat and simmer 10 minutes.
Add cheese, cayenne pepper, cook 2 minutes or until cheese melts, stirring frequently. Remove from heat immediately once cheese has melted. Top each serving with chopped green onions, if desired.
Recipe by Alida's Kitchen at https://www.alidaskitchen.com/2012/01/31/lighter-cheesy-potato-soup-with-broccoli/