Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Toss the cubed butternut squash with olive oil, salt, pepper, and dried thyme on the baking sheet. Spread it out in a single layer.
Roast the squash in the preheated oven for 25 minutes, or until tender and caramelized, stirring halfway through for even cooking.
While the squash is roasting, cook the pasta in a large pot of salted boiling water according to package directions until al dente. Reserve 1 cup of pasta water and then drain the pasta in a colander.
Once the squash is done, transfer it to a blender or food processor. Add the vegetable broth and heavy cream. Blend until smooth.
In the pot where you cooked the pasta, combine the cooked pasta and butternut squash sauce. Stir well to coat all the pasta. If the sauce is too thick, add reserved pasta water a little at a time until you reach your desired consistency.
If using, stir in the grated Parmesan cheese until well combined. Adjust seasoning with salt and pepper as needed.
Serve the pasta hot, garnished with fresh sage leaves if desired.