Cook pasta in boiling water until al dente. During the last 5-7 minutes of cooking, add frozen peas and continue boiling both the pasta and frozen peas for 5-7 more minutes. Drain. Reserve ½ cup pasta water.
Tear prosciutto into smaller pieces.
In a large skillet, heat 2 tablespoons butter on medium heat. Add the torn prosciutto and stir to coat it with butter, for about 1 minute. Add black pepper. Add another 2 tablespoons of butter and stir until melted.
To the skillet with butter and prosciutto add drained cooked pasta with peas. Sprinkle ¾ cup shredded Parmesan cheese evenly over pasta. Stir everything together on medium heat until the cheese melts. If needed, add a small amount of pasta water (about ¼ cup) - but you might not need to.
Season with salt, if needed. Serve immediately, topped with the remaining ¼ cup shredded Parmesan cheese