batali's pasta with spicy squash

http://www.foodandwine.com/recipes/cavatelli-with-spicy-winter-squash

Ingredients

1. 1/4 cup plus 2 tablespoons extra-virgin olive oil
2. 6 large garlic cloves, thinly sliced
3. 1 large red onion, thinly sliced
4. 2 teaspoons crushed red pepper
5. 2 pounds butternut squash—peeled, seeded and cut into 1/2-inch cubes
6. 1 tablespoon finely chopped thyme
7. Salt and freshly ground pepper
8. 1 1/2 pounds cavatelli or small shells
9. 3/4 cup freshly grated caciocavallo, pecorino or Parmesan cheese, plus more for serving

1. Bring a large pot of salted water to a boil. In a large, deep skillet, heat the olive oil. Add the garlic, onion and crushed red pepper and cook over moderately high heat, stirring occasionally, until the garlic and onion are softened, about 5 minutes. Add the squash and thyme, season with salt and pepper and cook for 5 minutes, stirring occasionally. Cover and cook over moderately low heat, stirring occasionally, until the squash is tender, about 5 minutes.
2. Meanwhile, add the cavatelli to the boiling water and cook until al dente. Drain, reserving 1 cup of the pasta cooking water. Add the cavatelli to the squash mixture in the skillet, then stir in 1/2 cup of the pasta cooking water and toss gently to combine. Add the 3/4 cup of caciocavallo, season with salt and pepper and stir gently; add a little more pasta water if necessary. Serve the pasta right away, passing more cheese at the table.