Preheat your oven to 400°F (200°C). Place the cubed butternut squash on a large baking sheet. Add the unpeeled garlic cloves, drizzle with olive oil, and sprinkle with chopped sage, salt, pepper, and nutmeg. Toss everything together until the squash is evenly coated.
Spread the squash in a single layer and roast for 25-30 minutes, stirring halfway through, until the squash is fork-tender and beginning to caramelize at the edges.
While the squash is roasting, bring a large pot of generously salted water to a boil. Cook the pasta according to package instructions until al dente. Before draining, reserve about ½ cup of the starchy pasta water.
In a large skillet over medium heat, add the tablespoon of olive oil and sauté the diced onion until translucent, about 3-4 minutes. Add the minced garlic and cook for another 30 seconds until fragrant.
Once the butternut squash is roasted, remove from the oven and let cool slightly. Squeeze the roasted garlic cloves from their skins. Transfer the roasted squash, roasted garlic, and all the flavorful oil and bits from the baking sheet to a blender or food processor.
Add the broth to the blender and blend until smooth and velvety.
Add the butternut squash puree to the skillet with the sautéed onions and garlic. Stir in the heavy cream and bring to a gentle simmer.
Add the drained pasta directly to the sauce along with a splash of the reserved pasta water. Toss everything together, adding more pasta water as needed to reach your desired consistency.
Fold in the Parmesan cheese and fresh thyme leaves. Taste and adjust seasoning with salt and pepper if needed.
Transfer the pasta to serving bowls. Garnish with crispy sage leaves, toasted pine nuts or pumpkin seeds, additional Parmesan cheese, and a light drizzle of high-quality olive oil. Add red pepper flakes if desired.