Peel and finely slice the potatoes using a mandoline or a sharp knife. Brush the base and sides of a tin or dish about 20cm square with the butter, and line with parchment.
Heat the oven to 180C/160C fan/ gas 4. Add the potatoes, overlapping slightly in layers, and drizzle over the extra butter and some seasoning every few layers until all of the potatoes and butter are used up. You should have seven or eight layers. Cover tightly with foil. Cook for 40-50 mins until a sharp knife goes easily through the layers. Leave to cool, then put a plate that fits in the tin on top of the foil with some cans or a chopping board on top to weigh it down, and chill for at least 6 hrs or overnight. About 30 mins before frying, transfer the tin to the freezer to firm up even more.
Put the oil in a heavy-based deep pan so it’s no more than half-full, and heat to 180C on a cooking thermometer or until a cube of bread sizzles immediately and browns in 30 secs when lowered in.
Tip the potato block from the freezer out onto a board and remove the parchment. Cut into thick chips and lower into the hot oil in three or four batches and cook for 4-5 mins until golden and crisp. Try not to move the chips around in the pan too much. Scoop out onto kitchen paper and season. Set aside while you cook the rest (don’t keep uncooked chips next to the hot pan or the butter will melt).
Mix the chilli mayo and crab dips, if serving both, or dollop a little soured cream on each chip, and top with a little apple sauce and dill.