In a large saucepan, combine water, potatoes, onion, basil, chicken bouillon granules & pepper.
Bring to a boil, reduce heat. Cover and simmer for 15 minutes or until potatoes are tender.
Remove from heat, DO NOT drain. Using a potato masher or fork, mash potatoes in saucepan.
Stir in broccoli, return to boiling. Reduce heat; cover and simmer 8-10 minutes or until broccoli is tender.
Stir in chopped ham, light cream or half & half, and butter.
Cook and stir until heated though.
To serve, ladle into soup bowls. Sprinkle each serving with parmesan cheese.