Mix water and cream of tartar in a large bowl.
Stir potatoes into water mixture until potatoes are well coated; drain.
Layer potatoes and onion in a slow cooker; season with salt and black pepper.
Heat milk and flour in a saucepan over medium heat, stirring often, until boiling, about 5 minutes; season with salt and black pepper.
Pour about half the milk sauce over the potato mixture.
Scatter Cheddar cheese and ham into the slow cooker; cover with remaining milk sauce.
Cook on Low setting for 9 to 10 hours or on High for 4 1/2 to 5 hours.
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