Heat a large, deep skillet over medium heat.
Add the olive oil, garlic, thyme and red pepper flakes, and saute until fragrant.
Add the chopped butternut squash and stir until coated.
Add the chicken stock and cover. Let simmer for about 15-20 minutes, or until the butternut squash is soft.
Meanwhile, set a large pot of salted water to boil and cook pasta according to package directions.
When the butternut squash is soft, turn off the heat under the skillet and allow it to sit uncovered for a few minutes.
Add the cream and parmesan, stir well, and puree with an immersion blender until the sauce is silky smooth (using a regular blender works too!)
Drain the pasta and add it into the skillet , tossing it well in the sauce to coat.
Sprinkle the top with some more freshly shredded parmesan, few sprigs of fresh thyme, and additional red pepper flakes, if desired.