Combine flour, sugar, butter and egg yolks in the bowl of a food processor. Blend until it forms a ball then use your hands to shape it into a disc.
Wrap in cling wrap and refrigerate for 1 hour.
Preheat oven to 180ºC. Melt the butter in a 24 cm heavy-based, ovenproof frying pan. Add the sugar and stir over a medium heat until dissolved. Increase the heat to medium – high and cook for 8 – 10 min until it turns into a golden caramel. Carefully add the apple pieces to the pan (the caramel may splutter and spit) and cook for a further 8 min, or until the apples are slightly soft, but not mushy.
To make pies
While the apples cook, roll pastry out to a circle, slightly larger than frying pan.
Remove pan from heat and arrange the apples over the surface. Cover with pastry. Bake for 20 – 25 min, or until the pastry is golden brown.
Remove from the oven and cool for 15 min. To serve, invert the tart onto a serving plate, drizzle with Calvados (if using) and serve with ice cream or plenty of whipped cream.