Cook pasta as instructed on the package; take it out just before it is al dente. Reserve 1/2 cup of pasta water, but don’t throw away the rest of the water yet.
Mix the whole eggs, yolk, pecorino, parmesan, and seasonings in a large heatproof bowl. Set aside.
In a large skillet, melt the butter over medium heat. Add the garlic and brown (approx. 3 minutes). Add the pasta to the pan and mix well so that all the pasta is coated with butter.
Then add that pasta to the bowl with the egg and cheese mixture, also adding the reserved pasta water, and mix well.
Place the bowl over the pot of simmering pasta water (making sure the bottom of the bowl does not touch the water) and cook with steam, stirring and scraping the sides of the bowl constantly with a rubber spatula, until the sauce is thickened and has a creamy consistency. Stir for about 1 minute, adding more pasta water if necessary to adjust the consistency of the sauce.
Remove the bowl from the heat, add the parsley, mix well again and serve.
