Clean and rinse the parsley, once dried chop it finely. Toss the pasta in a large saucepan with plenty of boiling salted water and cook it al dente. In the meanwhile brake the eggs in a bowl, pour the milk in it and whisk gently with a fork.Add a pinch of salt and a grind of pepper, half of the parmesan and mix well. In a different pan, heat the chunks of butter, once drained, add the pasta, flavour it with a wooden spoon. Remove the pan from the heat pour the egg and cheese mix.Put the pan back on the heat, sauté the pasta for a few seconds, sprinkle it with leftover parmesan and the chopped parsley. Arrange the pasta with sauce in a serving dish and serve immediately.