In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes, or until the onion becomes translucent. Next, add the minced garlic, cooking for an additional minute until fragrant.
Add the peeled and diced butternut squash to the skillet. Stir well to combine with the onions and garlic. Cook for about 5-7 minutes, allowing the squash to soften slightly.
Pour in the chicken stock or vegetable broth, and add the thyme and bay leaf. Bring the mixture to a gentle boil, then reduce the heat to a simmer. Cover and cook for about 15-20 minutes, or until the squash is tender.
Once the butternut squash is tender, remove the bay leaf and use an immersion blender or transfer the mixture to a regular blender. Blend until smooth and creamy. If using a regular blender, be cautious with the hot liquid—blend in batches if necessary.
Return the blended sauce to the skillet over low heat. Stir in the grated parmesan cheese and heavy cream. Season with salt and pepper to taste. Allow the sauce to warm through, about 2-3 minutes.
Toss the cooked pasta into the skillet with the creamy butternut squash sauce. Mix until the pasta is well coated. Let it cook for another minute, allowing the flavors to meld together.