Meanwhile, cook pasta shells according to package instructions, just until al dente. Drain water then lay shells out on a large cookie sheet lined with parchment paper. Let shells cool completely.
In a large bowl add chicken, garlic powder, salt, pepper and chopped broccoli. Toss to combine. Pour in 1 cup of the Alfredo sauce and stir together. Grease a 9x13-inch baking dish. Fill each shell with a large spoonful of the chicken and broccoli mixture and place side by side in the prepared dish.
Pour the remaining Alfredo sauce evenly over the shells. Sprinkle tops with the Mozzarella and Parmesan cheeses. Bake, uncovered, at 350 degrees F. for 25 minutes or until warm and bubbly. Serve and enjoy!