Beat together the butter, ½ cup sugar, the eggs and the cinnamon. Add the flour. Butter a pan and spread half of the mixture. Pass the apples through the onion grater and add them to the pan. Sprinkle the sugar which you have kept apart over the apples and add the rest of the mixture. Bake the apple pie for 35-40 minutes in a medium oven and when it has cooled off, sprinkle with the caster sugar.