To a large pot filled with water, add the salt. Bring to the boil. When boiling add the spaghetti, and cook until al dente.
While the pasta is boiling, add your bacon to a COLD large frypan or sauté pan, and put on medium heat. This will help render out all the fat we need to emulsify the sauce. Add pepper to the pan, when the bacon is halfway done.
In a separate bowl, add eggs, egg yolks and the finely grated pecorino romano together and mix until well combined.
Once the bacon has reached your liking of doneness, remove the pan from the heat. Once cooked to al dente, add the drained pasta (reserving some of the cooking water) to the bacon pan, and mix thoroughly so the pasta is well coated by the bacon fat. Now test the pan, and see how hot it is, you want the pan warm, but not hot, if you hear any sizzling or steam sputtering you need to wait awhile.
Add the reserved pasta cooking water, and the egg and cheese mix to the bacon pan and immediately vigorously mix (you don't want scrambled eggs). Mix vigorously for about 1-2 mins and you should see the sauce become creamy.
Serve in warm bowls, with a dusting more of black pepper and a good shave of the pecorino.