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Heat oven to 200C/180C fan/gas 6. Halve the pumpkin or squash, peel, deseed, then slice into 1cm slices. Toss with the oil in a roasting tin, season, then roast until tender and slightly charred at the edges. This can take up to 40 mins.
Meanwhile, make the tomato sauce. In a pan, soften the onion in the oil for 5 mins, then add the celery and garlic and cook for 1 min more. Add the tomatoes and sugar, then leave to simmer, uncovered, for 30 mins. Stir from time to time. You should be left with a thick purée. Season to taste.
Put the spinach in a saucepan with the water that still clings to it after washing, cover and put over a medium heat. Wilt the spinach for about 4 mins – you’ll need to turn it over with tongs every so often to make sure it all comes in contact with the heat at the bottom of the pan. When completely wilted, leave until cool enough to handle, then squeeze the water out with your hands. Chop and put in a pan with the butter. Gently heat, tossing together so the spinach is coated in butter, then season with salt, pepper and a generous grating of nutmeg.
For the béchamel sauce, bring the milk to the boil in a pan with the peppercorns, onion and bay leaf. Set aside for 5 mins to infuse, then strain the milk into another pan. Add the flour and butter, then gently heat, whisking all the while, until you have a thick, smooth sauce.
Heat oven to 200C/180C fan/gas 6 and assemble the lasagne. Butter a large gratin or baking dish, roughly 1.4 litres in capacity. Put a layer of pumpkin in the bottom followed by a layer of tomato sauce. Lay lasagne sheets on top of this, cutting them to fit if necessary (you don’t want any overlapping). Now add a layer of béchamel followed by a scattering of spinach and half the cheese. Top with more lasagne sheets, pumpkin, tomato sauce, more lasagne and a final layer of béchamel sauce. Sprinkle the remaining cheese over the top. Bake for 40 mins, or until the lasagne is golden and bubbling.