Set aside sauce packet from potato package. In a large saucepan, bring potatoes and 3 cups water to a boil. Reduce heat; cover and simmer for 10-15 minutes or until potatoes are tender. Rinse with cold water; drain thoroughly. Transfer potatoes to a bowl. Cover and refrigerate.
In a small saucepan, melt butter. Stir in contents of reserved sauce packet. Gradually add the remaining water; stir until smooth. Bring to a boil. Remove from the heat. Cover and refrigerate for 30 minutes. Stir in mayonnaise and mustard; gently stir into potatoes. Add eggs and sprinkle with paprika if desired. Refrigerate leftovers.