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Preheat the oven to 375°F. On a large, rimmed sheet pan, toss the squash with the garlic, the 3 tablespoons olive oil, and the salt, then roast until the squash is soft, about 30 minutes. Let cool slightly.
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Cook the spaghetti in a large pot of boiling water according to the package directions. Drain, reserving about 1 cup of the pasta cooking water. Return the pasta to the pot.
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Transfer the cooked squash to a blender or food processor. Add the chicken stock and chopped sage leaves. (If using a blender, hold a clean kitchen towel on top of the lid while blending hot liquid.) Blend until smooth and silky. If the sauce is too thick, add a tablespoonful or two of the pasta cooking water. Keep warm.
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In a small skillet, warm the 2 teaspoons olive oil over medium-high heat. Add the whole sage leaves and fry until the leaves are crispy and stop bubbling, about 1 minute. Immediately transfer to paper towels to drain.
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In the same skillet over medium
heat, toast the walnuts until fragrant and starting to turn golden, about
2 minutes, and add them to the paper towels with the sage.
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Toss the pasta with enough sauce
to coat generously, reheating over medium heat if needed. Distribute among 4 dinner plates and top with fried sage leaves and toasted walnuts.