Broccoli Cheddar Chowder

{Wisconsin would be proud}
I know it's a little out of season for soup and chowder, but given all the rain it just sounded good. Kinda like chili- but not.

Ingredients:
2 bunches (about 1 pound) fresh broccoli
1 medium onion, chopped
1/4 cup butter
1/2 cup butter
1/2 cup flour
4 cups milk (you could probably get away with 2 or 3)
1 cup chicken broth
1 1/2 teaspoon salt
2 cups grated cheddar cheese

Directions:
Cook broccoli just until tender. Do not overcook. Drain and cut into small pieces; set aside. Saute onion in the 1/4 cup butter until tender; set aside. In a large saucepan or soup pot prepare a white sauce: melt the 1/2 cup butter over medium heat, then stir in flour until well blended. Gradually stir in milk, chicken brother, and salt. Stir constantly until mixture reaches a boil. Cook 1 to 2 minutes, until thickened. Add broccoli and onion. Stir in cheese. cook briefly over medium heat. Avoid bringing to a boil. Serve immediately or keep warm over low heat.