Preheat the oven to 375°. Butter a 15-by-10-inch ceramic baking dish. Cut off the bulb end of the squash and halve it lengthwise. Scoop out the seeds. Drizzle the halves with olive oil and season with salt and pepper. Set the squash halves on a small baking sheet, cut side down, and bake in the lower third of the oven for 30 minutes, or until tender. Scrape the squash flesh into a medium bowl and mash with a fork.
Meanwhile, peel the squash neck and halve it lengthwise. Using a sharp knife or a mandoline, slice the squash crosswise 1/8 inch thick. Lightly oil 2 large rimmed baking sheets and arrange the squash slices on them. Cover with foil and bake in the upper third of the oven for 12 minutes, or until tender. Reduce the oven temperature to 350°.
In a large saucepan, bring the water to a boil. Add the 2 tablespoons of olive oil and slowly add the polenta, whisking constantly until smooth. Reduce the heat to low and whisk until thickened, about 5 minutes. Whisk in the mashed squash. Stir in 6 tablespoons of the butter and 1 cup of the Parmesan and season with salt and pepper. Spread the polenta in the prepared baking dish and arrange the baked squash slices on top in an overlapping pattern.
Cut the remaining 2 tablespoons of butter into small pieces and scatter them over the gratin. Sprinkle the remaining 1/3 cup of cheese over the top and bake in the upper third of the oven for 1 hour, or until bubbling and golden. Let stand for 15 minutes before serving.
The recipe can be prepared through Step 3 and refrigerated for up to 5 days. Bring to room temperature before baking.
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