In a frying pan large enough to hold the finished product, heat the oil over medium heat.
Add the pancetta (or bacon) and garlic and saute until it is brown and crisp, about 8 minutes.
Cool slightly. (if using bacon, remove from pan to drain on paper towel and discard the bacon fat in the pan)
Bring a large pot of salted water to a boil over high heat. Add the linguine and cook until it is just tender but still firm to the bite, stirring occasionally, about 10 minutes. Drain.
While the pasta is cooking, whisk together the cream, cheese, yolks, basil, and parsley in a large bowl. Set aside.
Add the cooked chicken to the pan with the pancetta or bacon
Next, add the spaghetti and the cream mixture and toss over medium-low heat until the chicken and sauce is heated through and the sauce coats the spaghetti thickly, about 4-6 minutes (do not let the mixture come to a boil)
Season the pasta, to taste, with pepper and salt if needed
Sprinkle the lemon zest over the pasta and serve.