Bring a large pot of water to a rolling boil over high heat.
In a large saute pan, combine olive oil, butter, onion and a pinch of salt and cook over medium heat until the onion has released all of its flavor into the fat and starts to become translucent, about 5 minutes.
Add the peas and prosciutto and cook, stirring often for about 3 minutes, or until the peas are bright green and tender. Reduce the heat to low while you cook the pasta.
When the water has come to a rolling boil, salt it so it tastes like a seasoned soup. Add the pasta and cook until al dente.
Meanwhile, in a small bowl, whisk together the eggs, yolks and Parmigiano. Add some pepper and whisk until smooth.
Using a spider strainer, transfer the al dente pasta to the skillet, then add the cream. Cook for 2 minutes over medium-low heat, then remove from the heat. Add the egg mixture (make sure the heat is off, you don’t want scrambled eggs) and mix with the passion of the Italian. Add a splash of pasta cooking water as needed to keep it smooth and glossy.
Serve in warm pasta bowls topped with a scrunch of pepper.