Start by bringing a large pot of salted water to a boil. Cook the rigatoni until it’s just shy of al dente—this ensures it won’t get mushy during baking. Drain the pasta well and set it aside.
In a saucepan over medium heat, combine the cheese soup, evaporated milk, heavy cream, and minced garlic. Stir until the mixture is smooth and begins to bubble gently. Lower the heat and simmer for about 5 minutes. Add the mozzarella, Parmesan, and black pepper, stirring until the cheeses melt into a creamy, velvety sauce.
In a large mixing bowl, combine the cooked pasta, shredded chicken, cream of chicken soup, and prepared cheese sauce. Toss everything together until the pasta is evenly coated and the chicken is well distributed.
Grease a 9×13-inch baking dish and pour in the pasta mixture. Spread it out evenly, then sprinkle extra mozzarella and Parmesan on top for a cheesy crust.
Preheat your oven to 350°F. Bake the casserole uncovered for about 45 minutes, or until the top is bubbly and golden brown. Let it cool for a few minutes before serving.