1. Rinse broccoli florets. Put enough water in the bottom of a 2 quart sauce pan to cover the bottom. Add broccoli and salt to taste if desired. Cook over medium heat until tender. Drain and set aside. 2. In a 3 quart saucepan, melt butter over medium heat. Stir in flour and salt and pepper. Gradually stir in milk, half and half, and chicken broth. Cook, stirring constantly, until sauce thickens and begins to boil. 3. Add cheese. Stir until melted. 4. Add broccoli. Cover and simmer on low heat until broccoli begins to fall apart (About 20 - 30 minutes.)