Heat the oven to 350°F. With the skin still on, wrap the garlic loosely with foil and drizzle with 1 teaspoon of olive oil. Roast for 40 minutes until soft.
Heat the butter and 1 teaspoon olive oil over medium-high heat in a sauté pan (I use a cast iron pan). Add onions and sprinkle with a pinch each of salt and pepper. Stir frequently until the onions begin to soften, about 8 minutes. Lower the heat to medium and stir occasionally until they turn a deep golden color and are caramelized, about another 15 minutes.
Meanwhile, place the cubes of butternut squash in a glass 9- by 13-inch pan. Drizzle with 2 tablespoons olive oil and toss until all pieces are coated. Sprinkle with 1 teaspoon of both salt and pepper. Cook until fork tender, about 30 minutes.
Raise oven temperature to 375°F. Lay the prosciutto on a foil-lined baking sheet. Crisp in the oven for about 15 minutes, flipping once. Set aside.
Bring a pot of salted water to boil.
Squeeze the garlic out of their peels into a blender. Add half of the cooked squash and all of the caramelized onions. Then add chicken broth, cream, cheese, and nutmeg. Blend until smooth. Season to taste with salt and pepper.
Add bucatini to the boiling water, cook until al dente. Drain. Return to pot and toss with sauce and reserved cubes of squash.
In the same pan you used to cook the onions, heat 2 tablespoons of olive oil over medium high heat. Once hot, place the sage leaves in the oil. Cook until crisp, about 30 seconds, flipping once. Drain on a paper towel.
To assemble, use tongs to move noodles to individual plates, letting excess sauce drip off back into the pot. Crumble the prosciutto over the noodles. Top with two sage leaves each. Sprinkle with extra grated American Grana and ground black pepper. Serve immediately.