Bring a large pot of salted water to a boil. Add ziti pasta and cook according to package instructions until al dente.

Three minutes before the pasta is done, add the broccoli florets to the boiling water. Drain and set aside with the pasta.

Heat olive oil in a large skillet over medium-high heat. Season chicken pieces with salt and pepper. Add to the skillet and cook until golden and cooked through, about 6-8 minutes. Remove from skillet and set aside.

In the same skillet, add minced garlic and sauté for 30-60 seconds. Pour in chicken broth and heavy cream. Bring to a simmer and let it reduce slightly, about 5 minutes.

Return the cooked chicken, pasta, and broccoli to the skillet. Stir in grated Parmesan cheese and mix until everything is well coated with the sauce. Cook for an additional 2 minutes to heat through.

Serve the chicken broccoli ziti hot, garnished with extra Parmesan cheese if desired.