In a large pot, bring salted water to a boil. Add the spaghetti and cook according to package instructions until al dente. Reserve 1 cup of pasta water, then drain the spaghetti and set aside.
In a large skillet over medium heat, add the diced pancetta (or guanciale). Cook for about 3-5 minutes until crispy and golden, stirring occasionally. Add the minced garlic and sauté for another minute until fragrant.
In a bowl, whisk together the eggs, heavy cream, and grated Parmesan cheese until well combined. Season with salt and freshly ground black pepper to taste.
Reduce the heat to low and add the drained spaghetti to the skillet with pancetta. Quickly pour the cream mixture over the pasta while tossing continuously to coat the noodles evenly. If the sauce is too thick, gradually add reserved pasta water until the desired creamy consistency is achieved.
Remove from heat and serve immediately. Garnish with chopped fresh parsley and additional grated Parmesan cheese, if desired.