Preheat the oven to 425 degrees F. Toss the butternut squash with 2 tablespoons oil, 1/2 teaspoon salt and a few grinds of pepper on a baking sheet and bake, tossing halfway through, until tender and golden brown, about 30 minutes.
Meanwhile, heat the butter and remaining 2 tablespoons oil in a large heavy bottom pot over medium-high heat until the butter has melted. Add the whole sage leaves and fry until crispy, but still vibrant green, about 3 minutes. Use tongs to remove them to a paper towel-lined plate.
Add the onion to the pot and cook, stirring frequently to make sure the butter does not burn, until tender and fragrant, 3 to 5 minutes. Add the pasta and stir to coat in the butter and onions. Toast the pasta in the pan, stirring frequently, until golden brown in spots, about 4 minutes.
Pour in the wine and cook, stirring frequently, until the liquid has been absorbed, about 5 minutes. Add 1 cup broth, and cook, stirring frequently, until absorbed, about 5 minutes. Repeat 2 more times until all the broth is absorbed and the pasta is cooked to al dente. Fold in the butternut squash, chopped sage, Parmesan, 1 1/2 teaspoons salt and a few grinds of pepper and stir until combined and creamy. Garnish with fried sage leaves and walnuts if using.
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