Cook the pasta. Bring a large pot of water to a rolling boil and add 2 teaspoons of salt. Add your preferred pasta shape and cook it according to the package instructions until it is al dente. Reserve 1–2 cups of the starchy pasta water before draining. Set the drained pasta aside.
Prepare the sauce base. In a large saucepan, melt the butter over medium heat until it begins to sizzle. Add the minced garlic and sauté briefly for just a few seconds to release its aroma. Sprinkle in the all-purpose flour, whisking constantly for about 30 seconds to form a roux.
Build the sauce. Gradually pour in the milk while whisking to ensure a smooth mixture, followed by the heavy cream. Lower the heat and continue stirring until the sauce thickens to your preferred consistency, which should take 1–2 minutes.
Incorporate the cheese. Add the shredded parmesan cheese and cream cheese cubes to the thickened sauce. Stir gently until both cheeses are completely melted and integrated, creating a velvety, rich sauce.
Season to taste. Sample the sauce and adjust the seasoning with salt and freshly ground black pepper. Start with a couple of pinches of salt and a few dashes of pepper, adjusting to your taste.
Combine and coat. Add the cooked pasta and shredded chicken to the saucepan. Toss everything together until every noodle is evenly coated with the creamy garlic parmesan sauce. If the sauce appears too thick, stir in a bit of the reserved pasta water to achieve the desired consistency.
Serve and garnish. Dish out the chicken pasta onto serving plates, garnishing with freshly chopped parsley and a sprinkle of extra shredded parmesan cheese for an indulgent touch. Serve warm and enjoy!