In a 5-quart pot, melt butter over medium heat. Mix in flour, stirring constantly until a thick paste forms. Remove from pot, and set aside.
In same pot, combine water, bouillon cubes, chicken, broccoli, salt and pepper. Bring to boil over high heat. Reduce heat to medium low, and simmer for 45 minutes.
Stir in the flour mixture a little bit at a time until soup thickens. Simmer 5 minutes. Reduce heat, and stir in cream. Mix in cheese 1 cup at a time, and stir until melted.
