Bring a large pot of water to a boil; add salt and spaghetti, and cook until al dente, according to package instructions. Reserve 1 cup cooking water; drain.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Add pancetta and cook until golden, 6 to 7 minutes. Using a slotted spoon, transfer pancetta to a bowl.
Reduce heat to medium-low. Add remaining tablespoon oil, and heat until hot but not smoking. Add garlic, and cook until golden, about 3 minutes. Turn off heat.
Beat the egg yolks, heavy cream, and 1/2 cup Parmesan cheese in a medium bowl until combined. Add drained hot pasta and pancetta to skillet, and pour the egg mixture over. If pasta seems dry, add enough of the reserved cooking water to moisten. Season liberally with freshly ground black pepper.
Serve garnished with chopped parsley, additional cheese, and lemon zest, if desired.