Bring a large pot of salted water to a boil over medium-high heat. Preheat an oven. Place cubed butternut squash and onion on a large rimmed baking sheet, then drizzle with olive oil, Kosher salt, cinnamon, and black pepper. Toss, then roast until tender. Cool, transfer to a blender.
Carefully add roasted butternut squash, onion, and garlic to a blender. Add whole sage leaves, large egg, and water, then secure the lid and blend until very smooth.
Place grated Parmesan cheese in a very large mixing bowl along with large egg yolks and remaining black pepper. Stir very well, then set aside.
Add dried linguine pasta to salted boiling water, then cook according to package directions until al dente. Reserve pasta water. Drain. Cook bacon. Heat a skillet over medium heat. Add chopped bacon (or pancetta), then cook.
Add the cooked pasta to the egg and cheese mixture along with the butternut squash sauce. Add crispy bacon (or pancetta), reserving a bit for garnish, then give it a final stir. Taste, adjust seasoning as needed, then divide evenly between plates.
Sprinkle each bowl of carbonara with a little extra grated Parmesan and crispy bacon. Garnish with fresh or fried sage leaves (see note below) and lots of cracked black pepper. Enjoy immediately!