Preheat the oven to 180°C, fan 160°C, gas 4. Lay the Parma ham slices on a wire rack and put on a baking tray. Bake for 10 minutes until crispy.
Meanwhile, warm the olive oil in a large pan over a medium heat and add the onion, garlic and parsley. Fry for 5-10 minutes until the mixture is soft and golden, then remove from the heat.
Meanwhile, cook the pasta according to the pack instructions. Drain well and add to the pan with the onion mixture.
In a large bowl, whisk the eggs, egg yolk, crème fraîche and cheese together. Add to the pasta in the pan, stirring until the heat of the pasta has cooked the mixture. Crumble the crispy Parma ham into the pasta and garnish with fresh parsley.