Bring a large pot of salted water to a boil. Cook spaghetti until al dente according to package instructions. Reserve 1/4 cup of the pasta water before draining.

While the pasta cooks, whisk together egg yolks, the whole egg, and Parmesan cheese in a bowl until smooth. Set aside.

Heat olive oil in a large skillet over medium heat. Add diced bacon and cook until crispy, about 5-6 minutes. Remove the bacon with a slotted spoon and set it aside, leaving the rendered fat in the skillet.

Lower the heat to medium-low and sauté garlic in the bacon fat until fragrant, about 1 minute. Be careful not to burn it.

Add the drained spaghetti to the skillet, tossing to coat it in the bacon fat and garlic.

Remove the skillet from the heat. Gradually stir in the egg mixture, tossing quickly to create a creamy sauce. Add reserved pasta water, one tablespoon at a time, to achieve your desired consistency.

Stir in the cooked bacon and season with black pepper.

Transfer the pasta to serving plates. Garnish with parsley and additional Parmesan cheese if desired. Serve immediately.