In a medium mixing bowl beat together the whole eggs, egg yolks, black pepper, and 1 cup of the grated pecorino cheese. Set aside.
In an 8-quart stockpot bring the 10 cups water and 1 tablespoon of salt to a rolling boil. Once your water is boiling you can add your linguine noodles and cook until al dente. This will take about 10 minutes. While your pasta is cooking you can start cooking your bacon.
In a large 12-inch skillet, that is 2 inches deep, on medium heat add the diced bacon. Cook the bacon, for 9-11 minutes, stirring often or until golden and crispy. Using a slotted spoon remove the bacon from the skillet, placing it into a small bowl, leaving the rendered bacon grease in the skillet.
Turn off the heat to the skillet and add the minced garlic and cook for 1 minute until the garlic is soft and fragrant.
Remove 1 ½ cups of the starchy pasta water from the pot of cooked pasta and set aside. Add the cooked pasta to the skillet and toss it around to coat the pasta with the garlic.
Add the beaten egg mixture to the pasta and quickly toss the pasta with the egg mixture then add 1 cup of the starchy pasta water and toss the pasta until the sauce has coated the pasta and slightly thickened up. The heat from the pasta and the starchy pasta water will gently cook the eggs without scrambling them. You may need to add an additional ¼-½ cup of the starchy pasta water to thin out your sauce. You need to work fast and toss the pasta in the sauce a few times to really coat the pasta.
Transfer your carbonara pasta to a large serving bowl. Top with the remaining ¼ cup grated pecorino romano cheese, cooked bacon crumbles, and the fresh chopped parsley.