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1
Preheat oven to 450F.
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2
Halve squash lengthwise and seed, then cut crosswise into 1 1/2-inch-wide slices and season with salt.
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3
Roast slices, skin side down, in a shallow baking pan in middle of oven until tender and golden, about 50 minutes.
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4
Set aside 6 crescent-shaped squash slices for serving and keep warm.
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5
Cut flesh from remaining slices into 1/2-inch pieces, discarding skin.
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6
Bring broth to a simmer and keep at a bare simmer, covered.
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7
Meanwhile, cook onion in butter in a 4-quart heavy pot over moderate heat, stirring, until softened, about 6 minutes.
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8
Add rice, garlic, and cumin and cook, stirring, 3 minutes.
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9
Stir in 1/2 cup simmering broth and cook at a strong simmer, stirring frequently, until broth is absorbed.
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10
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.
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11
(There will be leftover broth.)
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12
Stir in squash pieces, then stir in cheese, salt, sage, and arugula and simmer, stirring, 1 minute.
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13
(If necessary, thin risotto with some leftover broth.)
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14
Serve risotto immediately, spooned over reserved squash slices.
