Steam broccoli in microwave until tender. Do not overcook.
Saute diced onion in a 5 quart Dutch oven in ¼ cup butter. Set the onions aside.
In a Dutch oven melt ½ cup butter, stir in flour and slowly add milk chicken broth and salt and pepper.
Stir until sauce comes to a boil. It will thicken after a minute or two.
Add broccoli, onions and cheese stirring frequently.
Serve with warm bread and enjoy!
