Preheat the oven to 425°F and line a baking sheet with parchment paper. Arrange the cubed butternut squash and garlic on the pan, then drizzle with olive oil and sprinkle with salt, pepper, and dried sage. Toss well to coat every piece.
Roast the squash for 25 to 30 minutes, stirring once halfway through, until completely tender. Meanwhile, cook the pasta in salted water until al dente and reserve 1/2 cup of the cooking water. Blend the roasted squash and garlic with the remaining olive oil until silky smooth.
Transfer the squash puree to a large skillet over medium-low heat. Stir in a splash of reserved pasta water at a time until the sauce reaches a smooth, spoonable consistency. Add the butter and Parmesan, stirring until melted.
Add the drained pasta to the skillet and toss until evenly coated. Stir in the fresh sage and red pepper flakes, then season with salt and black pepper. Serve warm with additional Parmesan if desired.
