In a mixing bowl, whisk together egg yolks, grated Parmesan, and optional cream until smooth.
Lower heat to low and return drained pasta to the skillet. Gradually pour in the egg and cheese mixture while stirring continuously.
Slowly add the cooked chicken back to the skillet. If the sauce is too thick, add reserved pasta water gradually until the desired creaminess is achieved.
Season with additional salt and black pepper to taste. Garnish with extra Parmesan cheese and chopped fresh parsley.
Notes
For a refined finish, serve with a light green salad or steamed vegetables.