Steam broccoli until tender (this can be done in the microwave 6 min 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 corn starch and water in a small bowl. Stir into the cheese mixture in the double boiler, and heat over simmering water until soup thickens.