Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
Heat the oil in a heavy large frying pan over medium heat. Add the pancetta and garlic and saute until it is brown and crisp, about 8 minutes. Cool slightly.
In a large bowl, whisk together the cream, cheese, yolks, basil, and parsley to blend.
Meanwhile, bring a large pot of salted water to a boil over high heat. Add the spaghetti and cook until it is just tender but still firm to the bite, stirring occasionally, about 10 minutes. Drain.
Add the chicken to the pan with the pancetta and stir to combine. Next, add the spaghetti and the cream mixture and toss over medium-low heat until the chicken is heated through and the sauce coats the spaghetti thickly, about 4 minutes (do not boil or you might end up scrambling the eggs). Season the pasta, to taste, with pepper and salt if needed (the pancetta will likely add all the salt you need). Transfer the pasta to a large wide serving bowl. Sprinkle the walnuts and lemon zest over, and serve.