Fill a pasta pot with water and boil.
While the water boils, cut the bacon into pieces and add it to a large skillet. Cook the bacon over medium-high heat until it gets crispy, about 5-8 minutes. Remove the bacon from the pan with a slotted spoon and place it on a paper towel lined plate, keeping the bacon fat in the pan.
Cut the chicken into bite sized pieces and add it to the pan with the bacon grease. Chop the garlic and add it to the chicken. Cook for 5-8 minutes until the chicken gets brown.
When the water boils, salt the water with 3 tablespoons of salt. Add the pasta to the large pot of salted water and cook 2-3 minutes less than the package directions.
In a small bowl, crack the 4 eggs and 1 egg yolk into the bowl and mix well. Add the cheese and black pepper to the bowl. Take a ladle of the water the pasta is cooking in and add it to the mixture, slowly mixing while you pour.
When the pasta is al dente (meaning "to the tooth") reserve one cup of starchy pasta water, and drain the pasta. Add the pasta directly into the pan with the chicken.
Turn the heat off and add the egg and cheese mixture. Toss with tongs and mix. Add the crispy bacon and peas to the pot and continue to stir until combined. If the pasta looks a little dry, add some of the reserved pasta water. Serve immediately with more black pepper and cheese.