Step 1Bring a large pot of salted water to a boil. Add the pasta and cook 2 minutes less than the package directs. Add the peas and cook for 2 minutes more.
Step 2Meanwhile, whisk the eggs in a large bowl until smooth. Add the cheese and mix until evenly incorporated.
Step 3Reserve ½ cup pasta cooking water. Drain the pasta and peas in a large colander and shake to cool slightly. Pour into the bowl with the egg mixture. Toss gently until evenly coated. For a thinner sauce, toss in the reserved water, 1 tablespoon at a time, until you get the consistency you want.
Step 4Season lightly with salt and generously with freshly ground black pepper. Fold in the prosciutto until laced through the noodles. Serve immediately.