Preheat the oven to 350°F.
Bring a large pot of salted water to a boil.
Add the jumbo shell pasta to the boiling water.
Cook the pasta until al dente, according to the package directions.
Drain the cooked shells thoroughly.
Rinse the shells under cold water to stop the cooking process and make them easier to handle.
Set the shells aside while preparing the filling.
In a large mixing bowl, combine the cooked chopped broccoli, shredded rotisserie chicken, garlic powder, salt, and ground black pepper.
Add the shredded mozzarella cheese and grated Parmesan cheese to the chicken and broccoli mixture.
Add 1 cup of Alfredo sauce to the filling mixture.
Stir until all ingredients are evenly combined.
Spread a layer of Alfredo sauce evenly over the bottom of a 9x13-inch baking dish.
Spoon the chicken and broccoli filling into each cooked jumbo shell.
Arrange the stuffed shells in a single layer in the prepared baking dish, placing them on top of the Alfredo sauce.
Spread the remaining Alfredo sauce evenly over the stuffed shells.
Cover the baking dish with aluminum foil, if desired, to help keep the shells moist while baking.
Bake for 20 to 25 minutes, or until the shells are heated through and the sauce is warm and creamy.
Remove the baking dish from the oven.
Allow the stuffed shells to rest for several minutes before serving.
Serve warm.