Preheat the oven to 375 degrees F. Grease a small baking sheet generously with grapeseed oil.
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.
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.
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.
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.