Preheat the oven to 200°C, fan 180°C, gas 6. Roll out the puff pastry on a lightly floured surface and cut out a 28cm circle. Place in the fridge to chill for 15 minutes.
In a bowl, toss the apple quarters with 55g of the sugar, the lemon juice and the vanilla extract. Set aside.
In a 24cm ovenproof frying pan, melt the butter over a medium heat and add the remaining sugar. Turn down to a gentle heat and leave, without stirring, for 4-5 minutes, until the mixture turns a golden caramel colour - don't worry if it looks as if it has separated, as this is normal. Remove from the heat.
Arrange the apples on top of the caramel, rounded side down, in a circular pattern. Cover with the pastry circle, tucking the edges inside the pan around the apples. Bake in the oven for 35 minutes, until puffed and golden.
Remove from the oven and leave to cool for 10 minutes. Invert a plate over the pan and turn over. Serve warm.
Cook’s tip: when rolling out pastry, roll from the middle upwards then the middle downwards before turning 90 degrees and repeating. This helps the pastry roll evenly.