Cook the Pasta: Bring a large pot of salted water to a boil. Add the spaghetti and cook until just tender. Reserve about one cup of pasta water, then drain the rest.
Cook the Bacon: Place bacon in a large skillet over medium heat. Cook until crisp and golden. Remove bacon and set aside, leaving the rendered fat in the pan.
Warm the Chicken: Add shredded chicken to the skillet with the bacon fat. Stir and cook for a few minutes until heated through and lightly coated in flavor.
Add the Garlic: Stir minced garlic into the pan. Cook briefly until fragrant, keeping the heat gentle so it stays sweet.
Mix the Sauce Base: In a bowl, whisk together eggs, egg yolks, Parmesan cheese, salt, and pepper. The mixture should look thick and creamy.
Combine Pasta and Chicken: Add drained spaghetti to the skillet with chicken and garlic. Toss well so everything mixes evenly.
Create the Sauce: Remove the pan from heat. Pour the egg and cheese mixture over the pasta. Toss quickly and continuously so the eggs turn silky instead of scrambling. Add reserved pasta water a little at a time until the sauce looks smooth.
Finish and Serve: Stir in the crispy bacon. Taste and adjust seasoning if needed. Serve right away while the sauce stays glossy and warm.
