Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish and set aside.
In a large pot of salted boiling water, cook the lasagna noodles until al dente according to package instructions. Drain and drizzle with olive oil to prevent sticking.
In a saucepan, melt the butter over medium-low heat. Stir in the heavy cream, minced garlic, garlic powder, Italian seasoning, salt, pepper, nutmeg, and crushed red pepper flakes. Bring to a gentle simmer and cook for 3-4 minutes, whisking constantly, until slightly thickened.
Stir in the grated Parmigiano-Reggiano cheese until melted and the sauce is smooth. Remove from heat and set aside.
In a large bowl, combine the ricotta cheese, egg, and 1 cup of shredded mozzarella cheese. Fold in the cooked, shredded chicken and 1/4 cup of the prepared Alfredo sauce until well combined.
Spread 1/2 cup of the Alfredo sauce onto the bottom of the prepared baking dish.
Lay out the cooked lasagna noodles on a flat surface. Spread about 1/3 cup of the chicken and cheese mixture evenly along each noodle. Roll up the noodles tightly and place them seam side down in the baking dish.
Pour the remaining Alfredo sauce over the top of the lasagna rolls, spreading it out evenly. Sprinkle the remaining 1/2 cup of shredded mozzarella cheese over the top.
Cover the baking dish loosely with foil and bake in the preheated oven for 25 minutes, or until the cheese is melted and bubbly.
Remove from the oven and garnish with fresh chopped parsley before serving.