Preheat the oven to 350 degrees F. Cook the jumbo shells in a large pot of salted water according to the package directions until they are al dente.
Heat the creamy alfredo sauce in a large skillet or saucepan until it simmers over medium heat, then season with pepper.
Stir in 1/2 cup parmesan cheese and the shredded mozzarella cheese. Heat until the cheeses melt. Add the chicken and broccoli.
Heat the cheesy mixture until it's warmed through.
Spoon the filling into the unbaked shells. Smear a little of the pasta sauce at the bottom of the dish.
Place the stuffed shells in the pan. These can be served immediately or baked (covered with aluminum foil) for 15-20 minutes.
Garnish if desired, and serve with a simple salad, soup, or garlic bread.