Steam broccoli until tender (can cook in microwave on high power, 6 minutes per pound). Place half-and-half and water in the top of a double boiler. Add cheese (cut in pieces), salt and pepper. Heat until all the cheese is melted. Add broccoli. Mix cornstarch and water in a small bowl. Stir into the cheese mixture in the double boiler, and heat over simmering water until soup thickens.