Boil apples in a saucepan with water and icing sugar. Once apples are soft, remove pan from heat and blend with a hand blender or in a food processor. 

Add apple juice and mix well. If you want it to look a little greener, add a drop of green food coloring; mix very well.

Pour mixture through a strainer into a rectangular container and freeze for 5 to 6 hours, until it's frozen around the edges but not completely through.

Remove from freezer and rake sorbet with a fork, mixing it up well. Alternatively scoop it out and blend in a food processor until smooth. Raking it gives you a granita texture; blending it makes it velvety and smooth. 

Refreeze. If desired, blend it twice for an even creamier texture. Remove from the freezer about 10 minutes before serving to soften it a little.