Dice 1 pound thick cut bacon slices. Heat a 12-inch skillet or 3 to 4-quart braiser over medium heat. Add the bacon and cook until crisp, about 7 to 10 minutes, stirring occasionally. Use a slotted spoon to remove the bacon from the skillet and set aside on a paper towel-lined plate. Reserve about 2 tablespoons of the grease in the skillet.
Season 2 boneless skinless chicken breast with 1/2 teaspoon salt and 1/2 teaspoon black pepper. Add chicken to the skillet directly in the bacon grease. Cook for 5 to 7 minutes per side, until chicken reaches an internal temperature of 165°F (74°C). Remove from pan and dice or shred.
Meanwhile, bring a large pot of water to a boil and season with 1 tablespoon salt. Cook 1 pound spaghetti according to package directions. Use a liquid measuring cup to reserve 1 1/2 cups of the pasta water and set it aside before draining.
In a small mixing bowl, whisk together 4 large egg yolks, 2 whole eggs, and 1 cup of the grated pecorino romano cheese.
Toss the drained pasta with cooked bacon and chicken in the skillet. Pour in the egg mixture and reserved pasta water, and toss together with the pasta for 2 minutes.
Serve hot, topped with remaining cheese, 1/2 teaspoon freshly ground black pepper, and 2 tablespoons chopped fresh parsley to garnish.
Notes
Worried about those eggs being raw? The residual heat from the pasta and the pasta water is enough to cook the eggs. If you are still worried, you can combine it all in the skillet and cook over medium heat for 2 minutes.