Break the two eggs into a bowl, adding the yolks and both cheeses.Whisk to blend well, set aside.
Bring a large pot of water to boil over high heat. Generously salt the boiling water, add the pasta and cook until al dente, 8 to 10 minutes.
While pasta is cooking, heat a large skillet, add the olive oil and the guanciale or pancetta, sauté until just starting to brown about 2 minutes. Add garlic and red pepper flakes and cook another 2-3 minutes more. Add the wine and cook until reduced by half. Set aside but keep warm.
When pasta is done, reserve about 1 cup of the water then drain the pasta and add the pasta to the large skillet and toss with the meat in the pan.
From the 1 cup of reserved water take 1/2 cup and slowly pour into the egg mixture while stirring briskly. This tempers the eggs and prevents them from scrambling when you add them to the hot pasta.
Pour the egg mixture over the pasta and toss rapidly to coat the pasta with the sauce. This is best done with tongs. If the sauce seems too thick then add a little more of the pasta water to get the consistency you like.
Season with coarsely ground black pepper and sprinkle generously with the Italian parsley.