Saute the onion and celery in butter in saucepan over medium heat until tender.

Add the flour, and salt and pepper, cooking and stirring until mixture is smooth and bubbly.

Add the broth and milk (all at once), stirring constantly until the mixture comes to a boil and begins to thicken.

Add the cooked broccoli (I like to steam mine then cool in cold water to preserve color), stirring until all is heated through.

Remove from the heat and stir in the cheese until melted and smooth (place back on heat briefly if necessary).