Preheat your oven to 350°F. Lightly grease a 9×13-inch baking dish with nonstick spray and set it aside.
Cook the pasta shells until al dente, following the package instructions. Drain and set aside.
In a large mixing bowl, combine the mozzarella and Parmesan cheeses, reserving 1 cup for later. Add the ricotta, egg, salt, and pepper, mixing until smooth. Stir in the cooked chicken until evenly incorporated.
Spread one 15-ounce jar of Alfredo sauce across the bottom of the prepared baking dish. Fill each shell with the chicken and cheese mixture, then place them in a single layer in the dish. Pour the remaining Alfredo sauce over the shells and top with the reserved cheese.
Bake for about 20 minutes, or until the cheese is melted, bubbly, and lightly golden.
Finish with a sprinkle of fresh parsley and serve right away.