To make the pastry, rub the 65g/2¼oz butter into the flour and salt with your fingertips until it resembles breadcrumbs. In a separate bowl lightly mix the vinegar with 150g/5½oz water then add this to the dry mix and combine to make a dough. Transfer to the freezer for 10 minutes.
While the dough is chilling in the freezer, flatten the remaining 250g/9oz butter by placing it between two sheets of greaseproof paper and using a rolling pin to squash it into a square shape less than 1cm/½in thick.
Roll out the chilled pastry dough to form a rectangle twice the size of the flattened butter square. Fold the pastry over the butter, then turn it 90 degrees and roll it out until it has doubled in length. Fold both ends into the middle, then fold once more (to ‘close the book’). Transfer to the fridge for 20 minutes.
For the topping, mix the lavender with the caster sugar to infuse. Take four of the apples, slice them into wedges and set aside. Cut the remaining apples into halves and place them on a cooling rack. Transfer to the fridge to oxidise slightly.
For the pastry, repeat the rolling and folding process another three times and return to the fridge.
Preheat the oven to 200C/400F/Gas 6.
For the topping, add the lavender sugar, 20g/¾oz water and lemon juice to a heavy oven-proof frying pan and heat until the sugar has dissolved and a light caramel has formed. Remove from heat, add the butter and salt and swirl the pan occasionally until combined (don’t stir as this can make the caramel crystalise).
Place the halved apples in the centre of the pan, cut side down. Arrange the apples wedges around the halves and return the pan to a low heat for five minutes, then set aside to cool slightly.
For the pastry, repeat the rolling and folding process one more time, then carefully roll it out to fit the pan. Place the pastry on top of the pan, trim any excess - leaving a small overhang to tuck down the inside of the pan.
Bake for 30 minutes, or until the pastry is golden and crisp. Remove the tarte tatin from the oven and turn out onto a plate (take care with this as the caramel will still be very hot) and allow to cool for five minutes before serving with a spoonful of clotted cream.