1Cook potatoes, onion, salt & pepper, until soft & onion is clear; drain. DO NOT DISCARD POTATO WATER. Put potato water into soup pot. Put potatoes in mixing bowl, beat until MOST of the lumps are gone.
2In microwave safe bowl, stir together cream cheese, milk & cream of chicken soup. Microwave on low for 1-3 minutes, stir until well blended. Pour this into potato water, stir over low heat until well blended. Slowly add small amounts of this mixture into potatoes in mixing bowl; blend until "soupy", then slowly pour this mixture into soup pot. Stir until well blended.
3Slowly stir in shredded cheese & ham. Stir until blended. Do a "taste test". Add more seasoning if desired. Simmer on low heat for 30 minutes, for flavors to meld; stirring occasionally to prevent sticking. Serve with crusty rolls as a main dish or with veggies as a side dish.