Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs for al dente. Reserve 1 cup cooking water, then drain.
Meanwhile, peel the butternut squash and shred on the large holes of a box grater. Combine the olive oil and pancetta in a large dutch oven over medium-high heat. Cook, stirring occasionally, until lightly browned, 4 to 5 minutes. Add the garlic and red pepper flakes and cook, stirring, until lightly toasted, about 1 minute. Stir in the marjoram, then the shredded squash and 1/2 teaspoon salt. Cook, stirring, until the squash is just tender, 3 to 5 minutes.
Add the pasta and 3/4 cup of the cooking water to the dutch oven. Cook, tossing, until the pasta is coated with the sauce, 1 to 2 minutes, adding the remaining cooking water as needed. Season with salt. Divide among bowls and top with the parmesan.