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Preheat the oven to 375 degrees F. Grease a small baking sheet generously with grapeseed oil.
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Cut 1 inch off the tops of the acorn squashes, and reserve the tops. Scoop out the seeds and all but ½ inch of the flesh from the inside. Discard the seeds and finely chop the flesh; set aside. Put the squash shells cut-side down on the baking sheet and bake until tender, 35 to 37 minutes. Let cool.
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Heat the oil in a large skillet set over medium-high heat. Add the onion, parsnip, apples, curry powder, salt, and pepper. Cook, stirring, until the onions are soft, about 4 minutes. Add the mushrooms and reserved squash flesh and cook until lightly golden, about 4 minutes. Remove the pan from the heat and stir in the parsley and walnuts. Set aside.
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Turn the squash shells right side up on the baking sheet and spoon the filling into each. Place the reserved tops on the baking sheet beside the filled shells.
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Bake until tender and the stuffed squashes begin to brown, about 15 minutes. Serve hot, with the squash “lid” next to the squash on the plate.