Combine the apples and cider in a medium, heavy saucepan. Bring to a boil, stirring frequently. Cover, reduce heat to medium, and cook 20 minutes or until apples are very soft. Spoon apple mixture into a small bowl; cool.
Combine milk, sugar, and salt in pan; bring to a simmer. Add rice and nutmeg; stir well. Reduce heat, and simmer 40 minutes or until rice is tender, stirring occasionally. Combine apple mixture, amaretto, vanilla, and eggs in a blender or food processor; process until smooth. Stir egg mixture into rice mixture; cook until thick (about 5 minutes), stirring constantly (do not boil). Spoon rice mixture into a large bowl; cover and chill 8 hours.