Pulse flour, butter, and salt in a food processor to a sandy texture.
Add the egg and water and pulse again briefly.
Knead the dough on a floured surface for 30 seconds until smooth.
Flatten the dough to 1cm thickness and chill in cling film for 30 minutes.
Preheat the oven to 220°C with a baking tray inside.
Roll the dough to 2mm thickness and line a 22cm tart ring.
Prick the base with a fork and chill for a further 20 minutes.
Heat butter, lemon juice, and 15g sugar until dissolved, then stir in Calvados.
Arrange apple segments in the tart and brush with the Calvados mixture.
Bake at 220°C for 10 minutes, then reduce to 200°C for 20 minutes.
Whisk cream, egg, and 50g sugar, pour into the tart, and bake for 10 minutes.
Cool for 1 hour, remove the ring, and dust with icing sugar.