Preheat oven to 350°F. Lightly grease a 9×13-inch baking dish.
Cook the 8 lasagna noodles according to package directions until pliable. Drain and lay the noodles flat on a sheet of parchment paper or a lightly oiled surface so they do not stick.
In a medium bowl, combine 3 1/2 cups shredded cooked chicken, the 15-ounce container ricotta cheese, 1/4 cup freshly shredded Parmesan cheese (half of the 1/2 cup), the 3 sliced green onions, 1 1/2 teaspoons dried Italian seasoning, 1 teaspoon salt, 1/2 teaspoon crushed red pepper flakes, 1/2 teaspoon black pepper, 1/4 cup Alfredo sauce (from the 15-ounce jar), and 1 cup shredded mozzarella cheese (from the 3 cups). Stir until evenly mixed.
Pour 1/4 cup Alfredo sauce into the bottom of the greased baking dish and spread it evenly.
Spread the chicken-ricotta mixture evenly over each lasagna noodle—divide the mixture into eight equal portions and leave a small border at the short ends of each noodle.
Tightly roll each noodle from one short end to the other and place the rolls seam-side down in the prepared baking dish in a single layer.
Pour the remaining Alfredo sauce from the jar evenly over the assembled lasagna roll-ups.
Sprinkle the remaining 1/4 cup Parmesan cheese and the remaining 2 cups shredded mozzarella cheese evenly over the top of the rolls.
Cover the dish loosely with aluminum foil (tent the foil so it does not touch the cheese) and bake covered for 20 minutes.
Remove the foil and bake an additional 10 minutes, until the cheese is bubbly. If you want a more browned top, broil for 1–3 minutes more, watching closely to prevent burning.
Remove from oven, let rest a few minutes, sprinkle with 1 tablespoon chopped fresh parsley, and serve.