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For Squash:.
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Preheat oven to 450 degrees.
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Halve squash lengthwise and seed, then cut crosswise into 1 1/2-inch-wide slices and season with salt.
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Roast slices, skin side down, in a shallow baking pan in middle of oven until tender and golden, about 50 minutes (you might actually need to do it a little longer).
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Set aside 6 crescent-shaped squash slices for serving and keep warm. Cut flesh from remaining slices and chop into 1/2-inch pieces, discarding skin.
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6
For Risotto:.
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Start risotto after squash has been roasting 40 minutes:.
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Bring broth to a simmer and keep at a bare simmer, covered.
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Meanwhile, cook the onion in the butter in a 4-quart heavy pot over moderate heat, stirring, until softened, about 6 minutes.
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Add rice, garlic, and cumin and cook, stirring, 3 minutes.
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Stir in 1/2 cup simmering broth and cook at a strong simmer, stirring frequently, until broth is absorbed.
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Continue simmering and adding broth 1/2 cup at a time, stirring constantly and letting each addition be absorbed before adding the next, until rice is creamy-looking but still al dente (it should be the consistency of thick soup), about 18 minutes total. (There will be leftover broth.).
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Stir in 1/2-inch squash pieces, then stir in cheese, sage, and arugula and salt and pepper to taste. Then simmer, stirring, 1 minute. (If necessary, thin risotto with some leftover broth.).
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Serve risotto immediately, spooned over reserved squash slices.