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Heat oven to 200C/fan 180C/gas 6 and roast the butternut squash with 1 tbsp oil for 25-30 mins until tender, then set aside.
Meanwhile, heat remaining oil in a large pan and cook the onions and garlic for 10 mins until soft. Remove two-thirds, then add the mushrooms, chestnuts and pearl barley to the pan. Sizzle for a few mins, pour in the stock, then bring to the boil. Bubble fiercely for 30 mins until the barley is tender and sticky and there is no liquid left. Stir in the soy sauce, season and set aside.
While the barley layer is cooking, make the other layers. Stir the zest, ricotta, soft cheese and a good amount of seasoning into the reserved onions until smooth. Take a third of the mixture and gently fold with the sage and roasted squash. For the final layer, boil the kettle, then tip half the spinach into a large colander. Pour over the boiling water to wilt, then repeat with the rest of the spinach. Tip the spinach onto a clean tea towel and squeeze out all the moisture you can. Roughly chop, then mix into the remaining ricotta mixture with the parsley.
To make the pie, brush a 900g loaf tin with a little oil. Make 3 long triplelayer strips of foil and lay these across the width of the tin to help you lift out the pie to serve. Tip flour and 3 tsp salt into the largest bowl you have and gently melt the butter, shortening and milk with 200ml water in a pan. Once melted, increase heat until bubbling fiercely, tip onto the flour, then quickly beat with a wooden spoon until combined. Don’t worry if some powdery bits remain. Once cool enough to handle, knead until it comes together, then tip onto your work surface. Set aside a third and roll the rest into a large rectangle – big enough to line the tin with a little overhanging.
Ease into the tin, pressing evenly into the corners and sides – you can be rough with it. Spoon in the spinach layer, smooth the surface, then repeat with the barley and finally the squash layer. Dome the squash mix slightly to give a rounded top. Roll out the remaining pastry to fit, brush the edges with some egg, then press the lid over the top. Trim the excess and crimp or pinch to seal, then decorate with pastry trimmings cut into leaves (add bay leaves, if using, when the pie has 30 mins left in the oven). Can be covered and chilled overnight.
Heat oven to 200C/fan 180C/gas 6 and put a large baking sheet inside. Brush the surface of the pie with egg, lift onto the heated baking tray and bake for 30 mins, then reduce the heat to 180C/fan 160C/gas 4 and bake for a further 1 hr 30 mins until the pastry is golden brown and feels hard. Stand for 15-20 mins while you get the rest of the meal ready – the pie will stay warm. Gently tip out the pie, or use the foil strips to lift out carefully. Carry to the table and slice thickly to serve.