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For the pastry, pulse together the flour, butter and a pinch of sea salt in a food processor until it reaches a sandy texture. Add the egg, 1 tsp cold water and pulse again briefly. If you over-mix the dough at this stage it will lose its flakiness. Transfer the dough onto a lightly floured work surface and knead with the palms of your hands for 30 secs, or until smooth and well combined. With the palm of your hand, flatten the dough slightly to 1cm thickness, then sandwich it between 2 large sheets of cling film. Place on a baking tray and chill for 30 mins.
Roll the chilled dough, still sandwiched in cling film, to a 2mm thickness. Place a 22cm/3-4cm deep loose-bottomed cake tin on a baking tray. (Or use a 22cm/2-3cm deep tart ring and place on a greaseproof-lined baking tray.) Remove the top layer of cling film. Carefully pick up the dough and place it into the tin with the second layer of cling film facing up. Lift and tuck the dough into the edges of the tin and discard the cling film. By tucking in the base you minimise the shrinking of the dough during cooking. Trim off any excess with a rolling pin. Using your index finger and thumb, pinch and press the dough until it is 2mm above the tin all around the edge. Prick the bottom of the tart with a fork. Chill in the fridge for 20 mins.
Meanwhile, for the filling, heat the butter, lemon juice and 15g of the caster sugar in a small saucepan until the butter has melted and the sugar has dissolved. Remove from the heat and stir in the Calvados. Set aside. Heat oven to 220C/200C fan/gas 7. Place a baking sheet into the oven to pre-heat.
Arrange the apple segments in concentric circles over the chilled base, overlapping the apple slices as you go. Brush the apples all over with the Calvados mixture. Slide the tin or tart ring (on its lining paper) onto the pre-heated baking sheet and bake for 10 mins. Reduce the oven to 200C/180C fan/gas 6, then continue to cook for 15-20 mins more.
Meanwhile, whisk together the double cream, egg and the remaining 50g caster sugar until well combined. After the 15-20 mins baking – when the pastry is pale golden brown and the apples have started to caramelise – sprinkle the tart with the 1 tbsp caster sugar, then pour the custard mixture into the tart. Bake for a further 10 mins until the filling has just set.
To serve, remove the tart from the oven and set aside for 1 hr to cool slightly. Carefully remove the tin or tart ring and serve immediately with crème fraîche.