|Cook the potatoes until very soft, using the 2-qt. sauce pan and just enough water to cover. Cook, covered, reducing the heat to avoid scorching, after boiling starts. Scald the milk and onion in another sauce pan over moderate heat. Melt butter in Dutch oven, blend in the flour and add the milk, stirring to make a smooth sauce. Cook for 7 minutes.
Lift out the onion slices so that they do not go into the soup. Add the seasonings and the potatoes, which should be whipped to a granular consistency or rubbed through a colander-strainer. Cover and leave over very low heat until thoroughly hot. Serve with sprinkling of parsley and paprika on each serving.