Bring a large pan of salted water to the boil and cook the pasta as directed on the pack.
Meanwhile, heat the oil in a large pan over a medium heat and cook the bacon for 5-6 minutes until golden and crisp.
In a bowl, beat together the Philadelphia and egg yolks. Season generously with black pepper.
Drain the pasta, reserving some of the cooking water. Add it to the pan with the bacon and stir well to combine everything, adding a splash of the cooking water to loosen.
Remove from the heat and add the creamy Philadelphia mixture. Toss together again to coat the spaghetti in the sauce and cook the egg.
Divide amongst six bowls and top with the parsley and a few shavings of Parmesan.