Broccoli Cheese Soup-Jamie

1 (10oz) package frozen cut broccoli

3 tablespoons butter

3 tablespoons flour

2 cups half & half or milk

1/2 teaspoon pepper

1 cup grated medium Cheddar cheese

1 cup water

1/2 cup chopped onion

2 cups chicken

1 teaspoon salt

Steam broccoli in water until crisp and tender. Drain and reserve liquid. Measure liquid and extra water to make 1 cup. Melt butter in large saucepan. Add onion and saute' until soft, not brown. Blend in flour. Add broth and cook over medium heat, stirring occasionally until mixture boils. Stir in milk, salt and pepper. Add broccoli and heat until almost boiling. Turn heat very low and stir in cheese. Heat until cheese is melted.