Cook broccoli in large saucepan of boiling salted water until just tender, about 4 minutes. Drain. Melt butter in heavy large saucepan over medium heat. Add onion and cook until soft, stirring occasionally, about 8 minutes. Add flour and stir 2 minutes. Gradually stir in 2 cups broth. Slowly bring to boil, stirring frequently. Mix in broccoli, milk, half and half, Worcestershire sauce and hot pepper sauce. Return to boil. Thin with more broth if desired. Season with salt and pepper. Ladle soup into bowls. Top with some of cheese. Serve, passing remaining cheese separately. soup 40