Shell the peas, then start a pot of water for cooking the pasta as you prep the rest of the ingredients. When the water is boiling, start the pasta and heat a large skillet over a medium flame. Add 1 tablespoon of oil, then the prosciutto, tossing to coat with oil and separate the pieces. Cook for about 3 or 4 minutes, reducing the heat if it starts to smoke.
Add garlic to pan and cook until just fragrant, about 45 seconds. Add peas and toss to mix ingredients. Sauté for 1 or 2 minutes, then add cream. Toss to coat prosciutto pea mixture. The cream will pretty much disappear into the dish.
Drain fettuccine, reserving some cooking water, and add most of it to the pan. Toss to combine. Add the rest of the fettuccine gradually, making sure it doesn't overwhelm the other ingredients—if it starts to, discard the remaining pasta. If pasta is dry (mine was), add a little of the cooking water and toss to coat.
Divide among 4 shallow bowls, using tongs to pick up pasta. Much of the prosciutto pea mixture will remain behind in the pan. Use a spoon to top each serving of pasta with it. Grate some fresh Parmesan over each bowl and serve.