In a large skillet over medium heat, sauté the butter and onion until translucent. Add the prosciutto and cook until golden, but not crisp. Remove from heat.
In a separate bowl, beat the eggs and the cream until smooth, and then mix in the Parmigiano.
Bring a large pot of salted water to a boil. Cook the fettuccine until al dente. Drain it, retaining some of the cooking water.
Return the prosciutto and onion mixture to low heat. Add the pasta to the skillet. When thoroughly combined, add in the egg mixture and mix thoroughly. Add salt and pepper to taste. Add a bit of the retained cooking water only if necessary to achieve a creamy result.
Serve immediately with a sprinkle of Parmigiano and black pepper.