For the rough puff pastry, place the flour in a mound on a clean work surface and make a well in the centre.
Place the butter and salt in the well and work them together with the fingertips of one hand, gradually drawing the flour into the centre with the other hand.
When the cubes of butter have become small pieces and the dough is grainy, gradually add 125ml/4½fl oz of ice cold water and mix until it is all incorporated, but don’t overwork the dough – you should have a marbled effect with the butter without mixing it in properly.
Roll the mixture into a 2.5cm/1in thick rectangle, wrap in cling film and refrigerate for 20 minutes.
Flour the work surface and roll out the pastry into a 40x20cm/16x8in rectangle.
Fold the top third down to the centre, then the bottom third up to meet then fold the top over. Give it a quarter-turn.
Roll the block of pastry into a 40x20cm/16x8in rectangle as before, and repeat the folds. These are the first two turns. Repeat two more times to make four turns.
Wrap the pastry in cling film and refrigerate for at least 30 minutes before using.
For the tart, preheat the oven to 220C/425F/Gas 7.
Roll the pastry out on a lightly floured work surface to about 3-4mm thick. Cut into three rectangles of 7.5x15cm/3x6in and dust the pastry with icing sugar to cover totally.
Lift the pastry onto a baking tray and bake for 15 minutes. Meanwhile, make the filling.
Heat a small frying pan until hot, add the butter and apples and cook for a minute, then add 2-3 tablespoons of water and continue to cook.
Add the vanilla pod and seeds, blackberries and lemon juice and cook for 5-6 minutes, or until softened and pulpy.
Remove from the heat and cool in the fridge while the pastry cooks.
Whisk the double cream in a large bowl until firm peaks form when the whisk is removed from the bowl, then spoon into a piping bag.
Once the pastry is cooked, remove from the oven and leave to cool on a wire rack. Slice the cooled pastry sheets in half widthways through the length of the pastry - you have the same size rectangles as before but half as thick: one glazed piece and one bottom piece for each sheet.
Spoon the blackberry and apple mixture onto one layer of pastry, then pipe the cream over the top.
Place another piece of pastry on top and then repeat with another layer of blackberry and apple and cream.
Finish with a piece of glazed pastry. Repeat with the remaining pastry and the stacks can then be cut into portions to serve.