In a large saucepan combine water, potatoes, onion, basil, bouillon granules and pepper. Bring to a boil; reduce heat.
Cover and simmer 15 min, until potatoes are tender.
Remove from heat. Do not drain. Stir in broccoli. Return to a boil. Reduce heat; cover and simmer 8-10 min or until broccoli is tender.
Stir in chopped ham, light cream or half & half and butter. Cook and stir until heated thru. To serve, ladle into soup bowls. Sprinkle each serving with Parmesan cheese.