Preheat the oven to 350 degrees.
Heat a medium sized saucepan of water to boiling and cook the linguini according to the package instructions. Drain the pasta in a colander and set it aside until needed.
Melt the butter by placing it in a microwave-safe bowl and heating it in the microwave for 15 to 25 seconds.
In a large bowl, stir together the melted butter, the cooked chicken, the cream of chicken soup, the sour cream, the salt, the pepper, minced garlic, and the chicken broth. Use a wire whisk to stir these together.
Add the drained, cooked noodles to this mixture and stir them all together with a wooden spoon. Stir the mixture until the pasta is fully coated with the sauce.
Lightly grease a nine inch square baking pan with cooking spray. Spread the pasta, sauce, and chicken mixture in the baking pan. Sprinkle the Parmesan cheese and the Mozzarella cheese on the top of the pasta in an even layer. Add the parsley, sprinkling it over the cheeses.
Cover the pan with aluminum foil and bake it in the preheated oven for 25 minutes covered with foil. Take the foil off of the pan and return it to the oven, baking it for another 10 to 15 minutes, or until the cheese is lightly browned and the dish is bubbly.
Take the pan from the oven and let it cool for about 5 minutes before using tongs to scoop it out on to plates. Serve with a crusty roll and a side salad.