Preheat the oven to 350°F. Boil salted water in a large pot. Cook jumbo pasta shells according to package directions until al dente. Drain and set aside to cool.

In a mixing bowl, mix together the shredded chicken, ricotta cheese, egg, 1 cup of mozzarella cheese, 1/3 cup of Parmesan cheese, salt, and pepper until well combined.

Spread 1 cup of Alfredo sauce on the bottom of a 9x13-inch baking dish. Fill each pasta shell with a generous spoonful of the chicken mixture and place them in the dish.

Pour the remaining Alfredo sauce over the stuffed shells. Sprinkle the top with the remaining 1/2 cup of mozzarella cheese and 1/3 cup of Parmesan cheese.

Cover the dish with foil and bake for 25 minutes. Remove the foil and bake for an additional 10 minutes, or until the cheese is melted and bubbly. Let it stand for a few minutes before serving. Garnish with fresh parsley.