In a large pot of salted boiling water, cook the spaghetti according to package instructions until al dente. Reserve 1 cup of the pasta water and then drain the spaghetti.
In a mixing bowl, whisk together the eggs, grated Parmesan cheese, a pinch of salt, and a generous amount of black pepper until well combined. Set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced pancetta (or guanciale) and cook until it becomes crispy, about 5-7 minutes. Add the minced garlic and sauté for another minute until fragrant.
Reduce the heat to low. Add the drained spaghetti to the skillet with the pancetta and garlic. Stir to combine and remove the skillet from heat.
Quickly pour the egg and cheese mixture over the hot pasta while gently tossing to coat. The heat from the pasta will cook the eggs, creating a creamy sauce. If the sauce is too thick, gradually add the reserved pasta water until you achieve desired creaminess.
Divide the creamy carbonara into serving plates. Garnish with extra grated Parmesan cheese, freshly cracked black pepper, and chopped parsley.