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 (about 10 minutes) until it is just tender but still firm to the bite, stirring occasionally
Drain
Add the chicken to the pan with the pancetta and stir to combine
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