Photograph: Jan Baldwin
Roll out the pastry on a lightly floured surface to 3mm thick and cut out a 32cm circle, using a plate as a guide. Place on a baking sheet, lightly prick all over with a fork, wrap in clingfilm and freeze until ready to use.
Preheat the oven to 180°C, fan 160°C, gas 4. Add 40ml water to a 30cm flameproof and ovenproof Emile Henry tarte tatin dish (or ovenproof frying pan) and spoon the sugar evenly over. Let the sugar absorb the water for 1-2 minutes. On a medium-high heat, dissolve the sugar, then cook the syrup to an amber-coloured caramel (if it's too dark at this stage it will overpower the fruit). Take off the heat; stir in the 60g diced butter.
Arrange the apples very tightly in the dish – start at the edge, then fill in the middle, cutting the pieces to fit if necessary. Pack in as many as possible and press gently with your hands to make sure there are no gaps. Brush with the melted butter and cook on a baking tray in the oven for 30 minutes.
Remove from the oven, unwrap the disc of frozen puff pastry and place it on top. Tuck in the edges and prick a few holes in the top with a knife to let the steam out. Cook in the oven for a further 40-45 minutes until the puff pastry is golden brown and crisp.
Allow to cool at room temperature for about 1 hour before inverting on to a large serving plate, deep enough to contain the juices.