1. Preheat the oven to 425ºF. Cover a baking sheet with foil. In a bowl, toss the squash with the garlic, salt, pepper, rosemary or sage, and 1 tablespoon of the olive oil until all of the squash is coated with oil. Transfer to the baking sheet, place in the oven and roast for 30 minutes, or until tender and caramelized. Remove from the heat. Remove the garlic cloves and discard. Transfer the squash to a wide pasta bowl and add the cheese. Keep warm.
2. Bring a large pot of generously salted water to a boil and add the pasta. Cook al dente, following the timing instructions on the package but checking the pasta a minute or two before. Ladle about 1/2 cup cooking water from the pasta into the bowl with the squash and cheese and stir together.
3. When the pasta is ready, drain and toss with the squash mixture, the remaining tablespoon of olive oil, and the parsley. Serve hot.