Add the bacon to a large skillet over medium heat. Cook until crispy, about 8-10 minutes. Remove the bacon and transfer to a plate. Reserve 1 tablespoon of the bacon fat.

Whisk the eggs, egg yolk, reserved bacon fat, parmesan cheese, and black pepper in a medium bowl until smooth. Add 1/2 cup of the reserved starchy pasta water (see Step 3) to the egg mixture and whisk well. Set aside.

Bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente according to package instructions. Reserve at least 1 cup of the starchy pasta water, then drain the pasta.

Return the hot pasta to the pot or deep skillet (off the heat). Quickly pour the egg mixture over the hot pasta and toss vigorously to coat, ensuring the sauce is creamy and smooth. Add the crispy bacon and continue tossing to combine. If the sauce seems too thick, gradually add more reserved pasta water until it reaches the desired consistency.

Serve immediately, topped with extra parmesan, a sprinkle of parsley, and more black pepper if desired. Enjoy!