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1
Heat oven to 350F.
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2
Grease an 8x8 inch (2 quart) glass or ceramic baking dish.
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3
Cut the squash in half lengthwise and scrape out the seeds and fibers.
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4
Slice the squash and potatoes about 1/8 inch thick (use a mandoline if you have one).
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5
Line the bottom of the baking dish with a layer of squash (overlapping slightly), season lightly with salt and pepper, sprinkle with a little of the Parmesan, and drizzle with a little of the cream.
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6
Cover with a layer of potato slices, season with salt, pepper, cheese and cream.
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7
Repeat with the remaining squash and potatoes until the dish is full, ending with a top layer of squash, seasoned and topped with any remaining cheese and cream.
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8
(You may have extra squash, and extra potatoes if you used sweet potatoes!).
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9
Press down lightly to distribute the cream and compact the layers.
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10
The last layer of squash should be just sitting in the cream, but not covered by it.
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11
Cover the dish with foil and bake until the vegetables feel tender when poked with a thin, sharp knife (check the middle layer), about 1 hour, 10 minutes.
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12
Combine the walnuts and buttered bread crumbs.
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13
Remove the gratin from the oven, sprinkle with the breadcrumb-nut mixture, and bake until the top is lightly browned, 5 to 10 minutes.
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14
Let sit in a warm place for 20 minutes before serving so that liquids will set and tighten the gratin.
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15
Cut into 9 squares and serve.
