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Preheat oven to 350 F. Arrange hazelnuts on baking sheet and toast for 5 minutes. Once cooled, finely chop hazelnuts and drizzle with olive oil.
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In cast iron pot, heat 2 tablespoons olive oil. Add shallots and cook until golden brown and soft, around 8 minutes. Add garlic and red pepper and cook until fragrant and garlic is soft.
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Stir in squash. Add stock and bring mixture to boil. Reduce heat to simmer and cook until squash is tender, around 10 minutes.
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In another pot, bring salted water to boil. Add pasta and cook until al dente. Drain pasta and rinse with cold water.
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Once cooled, transfer squash mixture into blender and add 2 cups of Parmesan. Puree until smooth.
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Pour 1 cup squash puree onto 13x9 baking dish and spread all across. Add a layer of pasta then pour remaining sauce on top.
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Top with another 1/2 cup Parmesan, cover with foil and bake 15 minutes. Uncover and raise temperature to 425 degrees F and continue baking until the top has dark spots around, 12 minutes.
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Add basil, hazelnuts, salt and olive oil. Stir to combine and layer with more parmesan and pepper.