Preheat the oven to 180C/350F/Gas 4.
For the pie, place the flour and 175g/6oz of the butter into a food processor and pulse until the mixture resembles breadcrumbs. Add the egg, then add just enough water, one tablespoon at a time, to bind the mixture. Blend briefly to bring the mixture together as a dough.
Tip the dough out onto a floured work surface and knead gently. Shape into a ball and roll out into a flat circle with the thickness of a pound coin. Place onto a baking sheet lined with greaseproof parchment.
Arrange the sliced apple on the pastry, leaving a 2.5cm/1in gap around the edges, then sprinkle over the caster sugar and cinnamon and dot with the remaining butter. Draw the edges of the pastry up to form a crust and pinch to hold in place. Bake for 8-10 minutes in the oven, or until the pastry is golden-brown and crisp.
For the cinnamon cream, whisk the cream together in a bowl with the cinnamon and icing sugar until soft peaks form when the whisk is removed.
Serve the apple pie with spoonfuls of the cinnamon cream and a sprinkle of icing sugar.
