Let the pasta sit at room temperature until it becomes pliable, about 10 minutes. Meanwhile, heat the oil (if using) in a nonstick skillet over medium heat. Add the prosciutto or bacon (if using) and cook until crisp. Transfer to a paper towel-lined plate. Drain off and discard all but 2 teaspoons of the drippings in the skillet. Sprinkle the red pepper (if using) over the remaining drippings. Increase heat to medium-high. Add the pasta to the skillet and gently spread it out to form a large nest. Cook, without stirring, until the pasta begins to crisp and brown on the bottom, 4 to 5 minutes. Sprinkle with the Parmesan and prosciutto or bacon (if using). Cook, still without stirring, for about 2 more minutes. Season with the salt and black pepper. Slide or invert the pasta onto a plate and sprinkle with additional Parmesan. Cut into wedges, if desired.