Heat the oil in a heavy large frying pan set over medium heat. Add the pancetta and saute until brown and crisp, about 8 minutes. Remove the pancetta from the pan and set aside to cool.
Add the onions to the pan and cook until golden brown and lightly caramelized, 10 minutes. Add the garlic and 1/2 teaspoon of the salt and cook 2 minutes more. Set aside to cool slightly. In a large bowl, whisk together the gruyere, cream, Parmesan, lemon zest, eggs and the remaining 1/4 teaspoon salt.
Meanwhile, bring a large pot of salted water to a boil over high heat. Add the pasta and cook until just tender but still firm to the bite, stirring occasionally, 8 to 10 minutes. Drain, reserving 1 cup of the pasta water. Add the pasta back to the pan along with the onions, cream mixture, 1/4 cup of the reserved pasta water and the pancetta. Toss over low heat until the sauce is thick and coats the pasta, adding pasta water as needed, about 2 minutes (do not boil).
Season the pasta with lots of pepper. Transfer the pasta to a large, wide serving bowl. Sprinkle with chives and serve.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.