Preheat oven to 400 degrees. Toss cubed squash with 2 Tbsp. olive oil and salt and pepper to taste. Roast until tender and lightly browned, 25-30 minutes. Remove from oven and set aside.

Heat remaining 1 Tbsp. olive oil in a 12-inch skillet. Add the onion and sausage and cook over high heat, breaking up the sausage with a spoon, until lightly browned and cooked through. Add the roasted squash to the skillet.

Meanwhile, in a large pot of boiling salted water cook the pasta about 2 minutes less than package directions. Drain the pasta, reserving 1 cup of the cooking water. Add the cooked pasta to the skillet along with the reserved cooking water and the cheese and cook over moderately high heat, stirring, until the sauce is thick and creamy, 1 to 2 minutes. Transfer to bowls, sprinkle with parsley and serve immediately.