Bring 8 quarts of salted water to a rolling boil. Cook your pasta until al dente. In a medium bowl, whisk eggs, yolks, 1 tbsp cheese, and pepper. Set aside.
Meanwhile, in a large sauté pan, heat olive oil over medium heat. Add the onion, shallot, and garlic. Cook 5 minutes or until tender. Remove vegetables from pan and set aside. Add the pancetta to pan and cook over medium-high heat for 5 minutes, or until fat has mostly rendered and pancetta is crispy and golden. Add the prosciutto halfway through. Stir in onion mixture and stock and cook 4 minutes, scraping bottom of pan to loosen any browned bits.
Reserve ½ cup pasta water. Drain the pasta and toss with peas in pan over medium heat. Remove pan from heat. Stir in egg mixture to coat pasta. Add remaining 2 tbsp cheese and parsley and toss again. If the pasta looks dry, add reserved pasta water as needed. Transfer to a platter and serve immediately. Enjoy!