Bring a large pot of salted water to a boil over medium-high heat.
Roast the butternut squash. Preheat an oven to 425°F (220°C). Place cubed butternut squash and chopped onion on a large rimmed baking sheet, then drizzle with 2 Tbsp olive oil, 1 tsp Kosher salt, ½ tsp ground cinnamon, and ¼ tsp black pepper. Add 4 smashed garlic cloves, toss well, then roast until tender, about 20-25 minutes. Cool slightly, then transfer to a blender.
Make the butternut squash sauce. Carefully add roasted butternut squash, onion, and garlic to a blender. Add 4 or 5 whole sage leaves, 1 large egg, and ¼ cup of water, then secure the lid and blend until very smooth.
Mix the egg and cheese. Place 1 cup grated Parmesan cheese in a very large mixing bowl along with 4 large egg yolks and remaining ¼ tsp black pepper. Stir very well, then set aside.
Cook the pasta. Add 1 lb dried linguine pasta to salted boiling water, then cook according to package directions until al dente. Before draining, reserve 1 cup of pasta water. Drain. Meanwhile, cook bacon.
Cook the bacon. Heat a skillet over medium heat. Add chopped bacon (or pancetta), then cook, stirring occasionally, until crispy, but not burnt, about 4-6 minutes. Use a slotted spoon to transfer to a paper towel lined plate to drain.
Finish the carbonara. Add the cooked pasta to the egg and cheese mixture along with the butternut squash sauce. Use a spatula or wooden spoon to stir vigorously until very well coated. If needed, add about ¼-½ cup of reserved pasta water, then stir vigorously again until the sauce is thick and coats the pasta on all sides. 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.
Garnish, then serve. 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!