Cut apples into bit size pieces without the skin. Add the lemon juice,cinnamon and the sugar. Place the apples in a strainer with a pan underneath to collect the juice. Set it aside for 15 mins.
For the crust-place the flour,sugar and salt in a processor and pulse it 2 or 3 times. Add the butter in small pieces and pulse it again till it is crummy. with the prosser on slowly add the beaten egg (leave a spoon of the egg for the eggwash) and few spoons of the ice water .Stop when the crumbs start to form as dough (1 min). Remove the dough on cling flim ,flatten it little and refrigrate for 30 min.
Remove the juice that has collected under the apple mix into a pan mix in cornflour and slowly heat it till is turns into a thick syrup and set aside .
Preheat oven to 180'C .Lightly butter a muffin tin.Roll out the pie dough on a well floured surface to 1/4 " thickness. using a circular cookie cutter or a dish cut dough to the size that will fit into your muffin tin. Place the circular pie sheets into muffin holes.
Mix the apples with the syrup and spoon in one or two spoons of apple mix into the pie shells. cover with strips of pie doughs. Give a mild egg wash and bake for 20 min. Remove after 20 min and serve warm with a scoop of vanilla ice cream .