For the pork, preheat the oven to 150C/300F/Gas 2.
With a sharp knife, score the skin of the pork and rub with the olive oil, salt and black pepper.
Place the onion, carrot and leek into a deep-sided tray and pour in the water.
Place the pork on top, cover with foil and place in the oven for two hours.
Remove the foil and return to the oven for another three hours until tender and the crackling is crisp.
Remove from the oven and leave to rest for 30 minutes.
For the apple sauce, place the apples, butter and water into a saucepan, cover and place over a medium heat.
Cook until the apple has broken down – about 4-5 minutes.
Beat with a spoon to a purée, and then season with sugar and salt to taste.
For the Vichy carrots, place the carrots, butter, water and sugar into a pan and bring to a simmer.
Cover with a lid or cartouche (a circle of greaseproof paper arranged so that it covers the top of the carrots) and cook gently for 4-5 minutes, or until the carrots are tender. Season with salt and black pepper.
For the mash, place the potatoes into a pan of salted water, bring to the boil and simmer for 15 minutes, or until tender.
Drain and return the potatoes to the pan over the heat to drive off any excess moisture.
Mash well, add the butter and cream and beat to a smooth purée. Season with salt and black pepper.
To serve, spoon the mash into the centre of each plate, remove the pork from its cooking juices, slice it and pile it alongside the mash with a piece of crisp crackling. Finish with a pile of carrots, a spoonful of apple sauce and drizzle of any remaining pan juices.