Step 1

Preheat oven to 350°. Toast hazelnuts on a rimmed baking sheet or quarter sheet pan, tossing halfway through, until golden brown, 6–8 minutes. Let cool, then finely chop and transfer to a medium bowl. Stir in 2 Tbsp. oil; set aside.

Step 2

Heat remaining 2 Tbsp. oil in a medium pot over medium-high. Cook onion, stirring occasionally, until golden brown and softened, 8–10 minutes. Add garlic and red pepper and cook, stirring, until fragrant and garlic is softened, about 1 minute. Add squash and toss to combine. Add stock and bring to a boil. Reduce heat to medium-low and gently simmer until squash is tender, 12–15 minutes. Let cool slightly.

Step 3

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until very al dente, about 3 minutes less than package directions. Drain, then rinse with cold water.

Step 4

Transfer squash mixture to a blender. Add 1 cup Parmesan and purée until smooth; season with salt.

Step 5

Pour ½ cup squash purée into a 13x9" baking dish and spread to edges. Scatter pasta over sauce, then pour remaining sauce over. Top with ½ cup Parmesan. Cover with foil and bake 15 minutes. Uncover and increase oven temperature to 425°. Continue to bake until top is darkened in spots and sauce is bubbling, 10–15 minutes.

Step 6

Add basil to bowl with reserved hazelnuts, season with salt, and toss to combine. Spoon hazelnut mixture over pasta. Top with more Parmesan and black pepper.