Preheat oven to 375°F (190°C). Grease a 9x13-inch baking dish.
Cook jumbo pasta shells according to package directions until al dente. Drain and set aside.
In a large bowl, mix shredded chicken, ricotta, cream cheese, sour cream, 1/2 cup mozzarella, 1/2 cup Parmesan, egg, garlic, parsley, Italian seasoning, salt, and pepper until well combined.
Spread 1 cup of Alfredo sauce in the bottom of the prepared baking dish.
Fill each cooked pasta shell with the chicken mixture and place them in the dish seam side up.
Pour remaining Alfredo sauce evenly over the stuffed shells.
Top with the remaining 1/2 cup mozzarella and 1/4 cup Parmesan cheese.
Cover with foil and bake for 25 minutes. Remove foil and bake an additional 10–15 minutes, until cheese is melted and bubbly.
Garnish with fresh parsley before serving.