Preheat the oven to 400 degrees F and move the oven rack to the middle level.
Add 1 tablespoon of salt to a large pot of boiling water and add the dried pasta. Cook until "al dente" per the package directions.
Add fresh broccoli florets to the pasta water during the last two minutes of cooking. The broccoli should be bright green but not cooked through. *See notes for using frozen broccoli.
While the pasta is cooking, warm the alfredo sauce over low heat until heated through.
Drain the cooked pasta and broccoli in a colander and transfer to a large bowl.
Add the diced chicken, Alfredo sauce, and 1 cup of shredded mozzarella to the bowl. Stir to combine.
Spray a 13"x9" baking dish with cooking spray and pour the broccoli pasta mixture into the dish.
Top the ziti mixture with the remaining 1 cup of shredded cheese. Bake at 400 degrees F for 30-35 minutes until the Alfredo sauce is bubbling and the cheese is melty and golden brown.