Cook spaghetti in a 5-quart saucepan according to the package directions. Add the broccoli florets 2 minutes before spaghetti is al dente. (Use the cooking time given on the spaghetti package as a guideline). Drain and keep warm.
Add the ham, Alfredo sauce and pepper flakes to the pan and heat over medium heat until warmed, about 1 minute. Return the spaghetti and broccoli to the pan and toss to mix.
Spoon onto individual serving plates. Sprinkle with the Parmesan cheese and freshly grated pepper.