Cook the pasta. Cook your pasta in a pot of salted boiling water until al dente or according to package directions. Reserve 1/3 cup of the pasta water before draining the linguine or spaghetti.
Cook the bacon. Heat a large skillet over medium-high heat. Add the chopped bacon (or pancetta) to the skillet and cook for 4-5 minutes or until cooked to a desired crisp. Transfer the cooked bacon onto paper towels to drain. Leave about 1 tablespoon of bacon fat in the skillet and discard the remaining.
Cook the chicken. Slice the chicken into thin strips and season with salt and pepper. Add it to the skillet with the bacon grease and cook until golden brown, about 7 to 8 minutes. In the last minute, stir in the garlic and cook until fragrant. The chicken is cooked through when its internal temperature registers at 165°F. Remove the skillet from the heat.
Make the sauce. In a bowl, whisk the egg, egg yolk, parmesan, salt, and pepper. Gradually whisk in 3-4 tablespoons of the pasta water. Reserve the remaining water just in case you need it later.
Put it all together. The pan with the chicken should cool for 2-3 minutes before adding the egg sauce, so you don't end up with scrambled eggs. Add the egg sauce, bacon, and linguine to the skillet with the chicken, and stir quickly until all is combined. If needed, add more pasta water or stir in some heavy cream to make it creamier.
Serve. Serve the chicken bacon pasta warm with freshly grated Parmesan on top.
Notes
Sauce consistency: The thickness of the sauce depends on your personal preferences. Gradually add pasta water so you don't end up with a thin sauce.
Bacon options: For this recipe, you can use bacon or pancetta. Pancetta has a salty and rich flavor and a firmer texture. Bacon has a smoky, bold flavor, and if you are using it, make sure it is cooked until the fat is rendered.