Peel the butternut squash, then cut in half from top-to-bottom. Scoop out the seeds and set aside for another recipe, then slice the butternut squash in half, width ways, as close to the cavernous part containing the seeds. You should be left with two long, thin pieces, and two bulbous pieces. Cut the bulbous quarters into relatively small pieces, then season with salt and place in the oven.
Brush the two longer pieces with oil and place on a baking tray lined with greaseproof paper. Season with a pinch of salt and transfer to the oven and cook on the top shelf for around 30-40 minutes (dependent on size and shape) until almost cooked. Allow these pieces to cool down completely before using.
While the butternut squash is cooling, heat a splash of oil in a heavy-based pan and add the diced shallots. Cook over a medium-low heat for 3-5 minutes until soft and translucent, then add the sage, chopped mushrooms, and chestnuts. Season with salt and pepper, then continue to cook for another five minutes or so, then add a tablespoon or two of the breadcrumbs, and the chopped, roasted butternut squash, then mix to combine. Leave to cool.
Once the butternut squash pieces and the stuffing have cooled, roll out two sheets of puff pastry, large enough to generously host the filling. Sprinkle the remaining breadcrumbs between the two sheets, then top each with a layer of the stuffing (around the same width as the large squash pieces), then top with the butternut squash, followed by a little more stuffing to surround the squash.
Brush the edges of the pastry with some plant-based milk, then add another slightly larger layer of pastry to the top of each wellington. Gently press down and crimp the edges to seal, but be careful to avoid breaking the pastry. If the pastry does break, the gaps can be sealed with pastry offcuts.
Brush each wellington with plant-based milk, then make three shallow incisions to allow steam to escape while cooking.
Place the wellingtons in the oven and cook at 200C/Gas 6 for 30-40 minutes, or until golden brown. Leave to stand for five minutes before slicing.