Start by cutting the prosciutto into thin strips.
In a pan, melt the butter over low heat and add the finely chopped onion. Sauté it for two or three minutes, adding a little hot water to prevent it from burning. Now, add the prosciutto.
Let it brown on low heat for a couple of minutes, being careful not to burn it. Turn off the heat.
In a bowl, mix the two egg yolks with cooking cream, add the Parmesan cheese, and a generous grinding of black pepper, and whisk vigorously with a whisk or fork.
Boil the fettuccine in plenty of salted water and drain them very al dente, saving a good amount of cooking water. Transfer them to the pan with the prosciutto and toss them for about a minute, adding a ladle or two of cooking water.
Turn off the heat and add the cream and egg sauce, stirring immediately to prevent it from curdling. The sauce should be very creamy; if it dries out too much, you can further dilute it with some cooking water.
Serve the Fettuccine alla Papalina immediately, garnished with more pepper and Parmesan cheese, to taste.