Preheat the oven to 150C/300F/Gas 2.
Using a sharp knife, score the skin of the pork in strips. Rub the skin all over with olive oil then rub in the salt and thyme.
Place a deep-sided roasting tin on the bottom shelf of the oven then place the pork directly on a rack set just above and roast for five hours.
Increase the oven temperature to 210C/425F/Gas 7.
Meanwhile, remove the tin from under the pork (containing all the pork juices). Add the duck fat and return to the oven for five minutes, or until hot.
Place the potatoes into a large saucepan, cover with water, add a pinch of salt and bring to the boil, then simmer for a minute. Drain into a colander and shake around a little to rough up the edges.
Remove the tin from the oven and place over a high heat. Add the potatoes to the tin and turn them until coated in the fat. Return the tin to the oven and roast for 40-45 minutes.
While the potatoes are roasting, place the apple into a saucepan with three tablespoons of water, half the butter and two tablespoons of sugar. Cover and place over a medium heat and cook until soft and fluffy, stirring occasionally. Taste and add more sugar if desired.
Heat a frying pan until hot, add the last of the butter, the cabbage and a splash of water. Cook for a couple of minutes, or until the cabbage is tender and most of the water evaporated. Season with salt and black pepper.
To serve, carve the pork into thick slices and place onto plates. Spoon the potatoes alongside with a large dollop of apple sauce and cabbage.