Prepare Alfredo sauce by combining butter, garlic, heavy cream, and milk in a saucepan over medium heat.
Bring the mixture to a simmer, then remove from heat and stir in Parmesan and Mozzarella cheese.
Season with pepper, if desired.
Cook pasta shells according to the package instructions until al dente.
Drain the water, then arrange the shells on a parchment-lined cookie sheet to cool completely.
In a large bowl, combine cooked chicken, garlic powder, salt, pepper, and chopped broccoli.
Add 1 cup of the prepared Alfredo sauce to the chicken mixture and stir until well combined.
Grease a 9×13-inch baking dish.
Fill each cooled pasta shell with a generous spoonful of the chicken and broccoli mixture.
Arrange them in the baking dish.
Pour the remaining Alfredo sauce evenly over the stuffed shells.
Top with additional Mozzarella and Parmesan cheeses, then bake uncovered at 350°F for 25 minutes or until bubbly.
Serve hot!