Cook pasta in large pot of boiling salted water, stirring occasionally, until al dente, about 14-16 minutes. Add broccoli for the last 4 minutes. Drain, reserving 1-1/2 cups pasta water.
Meanwhile, place a large non-stick skillet over medium heat with enough olive oil to coat the bottom of the pan. Add prosciutto and sauté for 1 minute. Add cooked pasta, broccoli, Parmesan, and pasta water. Stir to incorporate. Season with salt & pepper. Serve and enjoy!