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Using a medium sized stock pot, boil potatoes until desired tenderness. Reserve 1 cup of water from boiled potatoes then drain.
In a small frying pan, sauté onion in butter until tender and translucent.
Add onions, butter and flour to stock pot and stir together over low heat to make a roux (thickener).
Add potatoes, reserved liquid, milk, cheese and Ham to stock pot and simmer on medium heat 30-40 minutes stirring frequently until thickened.
Serve with cornbread or fresh baked rolls. Garnish with shredded cheese.