Preheat oven to 375 degrees F. Spray a 9x13-inch baking dish with nonstick cooking spray; set aside.
Cook pasta shells according to package directions. Rinse with cold water and drain then set aside.
While pasta is cooking, make the alfredo sauce by melting butter in a skillet over medium-high heat. Add garlic and sauté for 1 minute, stirring frequently.
Add flour and cook for an additional minute. Whisk in milk until well combined. Bring to a low boil then reduce heat to medium-low, and cook for an additional 2 minutes, or until thickened. Add parmesan cheese, salt and nutmeg and stir until cheese is melted and sauce is smooth. Remove from heat and spread half the sauce in the bottom of the prepared pan; set the rest aside.
In a large bowl, combine ricotta, cooked chicken, egg, salt, pepper, 1⁄2 cup mozzarella and parsley. Fill shells with chicken mixture (about 1 Tablespoon of mixture per shell) and place in baking dish (they will overlap).
Once all shells are filled, pour remaining sauce on top of the shells in the pan. Top with remaining 1⁄2 cup mozzarella cheese and cover pan with foil. Bake for 20 minutes then remove foil and bake for an additional 10 minutes or until cheese is melted.