Step 1

Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs for al dente. Ladle 1 1/2 cups cooking water into a liquid measuring cup and set aside, then drain the pasta in a colander.

Step 2

Meanwhile, heat the olive oil and garlic together in a large pot or Dutch oven over medium-high heat. Cook, stirring, until the garlic is browned, 1 to 2 minutes. Add the squash and 1/2 teaspoon salt. Reduce the heat to medium, cover and cook, stirring occasionally, until the squash is very tender and starting to break down, 6 to 8 minutes.

Step 3

Add 3/4 cup of the reserved cooking water to the squash and bring to a simmer. Cook, stirring and breaking up the squash with a wooden spoon, until the sauce is slightly thickened, about 1 minute. Add the pasta and toss until well coated. Add more cooking water to loosen, as needed. Season with salt.

Step 4

Divide the pasta among bowls. Drizzle with more olive oil and sprinkle with the Parmesan.