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Put the mixed nuts into the bowl of a food processor and blitz until finely chopped, then tip out into a bowl. Alternatively, roughly chop using a knife. Put the carrot, celery and onion in a frying pan. Cut the long, thin half of the squash in half lengthways or into quarters (depending on how wide it is) and slice into long, thin slices using a sharp knife or mandoline (reserve the thicker bulb half of the squash for another recipe).
Drizzle the oil over the veg in the frying pan, then fry for 15-20 mins over a low-medium heat until golden and soft. Scrape the mixture into the chopped nuts and stir in 2 tbsp honey, the chestnuts and nut butter. Stir everything together, then season.
Oil a 20cm springform cake tin and line the base with baking parchment. Arrange 3-5 sage leaves in the tin, face-down. Finely chop the rest of the sage leaves and add them to the nut mixture. Arrange some of the squash slices in the base of the tin, laying them neatly so the layers overlap slightly to form a spiral pattern. Drizzle over ½ tbsp of the remaining honey. Spoon in half the nut mixture, pressing it firmly into the tin with the back of a spoon, then top with another layer of squash, this time in a single layer rather than overlapping – this will make it easier to cut later. Drizzle over the rest of the honey. Spoon in the remaining nut mixture and press it in firmly with the back of a spoon. Any remaining squash will keep in the fridge for up to three days to use in tarts and quiches, or to be grilled for salads.
Heat the oven to 180C/160C fan/gas 4. Cover the tin with foil and roast for 30 mins, then uncover and roast for another 20 mins until the top of is golden and crisp. Leave to rest for 15 mins, then invert onto a plate and cut into wedges to serve.