Cook pasta in a large saucepan of boiling salted water, following packet directions until tender. Drain.
Meanwhile, heat oil and butter in a large, deep frying pan over medium heat. Add garlic and walnuts. Cook, stirring, for 1 minute or until fragrant. Add pumpkin. Cook, stirring occasionally, for 2 minutes or until squash is tender.
Add cream and parmesan. Cook for 1 to 2 minutes or until heated through. Add spinach and pasta to squash mixture. Season with salt and pepper.