Preheat your oven to 350°F. While it heats, bring a large pot of salted water to a boil and cook the penne pasta according to package directions until al dente (usually 9-11 minutes). Drain the pasta and set aside—don't rinse it, as the starch helps the sauce cling to the noodles.
In a large mixing bowl, combine the softened cream cheese, milk, jarred alfredo sauce, minced garlic, Italian seasoning, salt, and pepper. Whisk everything together until smooth and well combined—the cream cheese should fully incorporate into the sauce. I like to warm the milk slightly before mixing to help the cream cheese blend more easily and create a silkier sauce overall.
Add the cooked pasta from Step 1 and the shredded chicken to the alfredo sauce mixture from Step 2. Stir gently but thoroughly to coat all the pasta and chicken evenly with the sauce. Then fold in 1.5 cups of the shredded mozzarella and 3/4 cup of the grated Parmesan cheese, stirring just until combined.
Pour the pasta and sauce mixture from Step 3 into a 9x13 inch baking dish, spreading it evenly. Top with the remaining 1.25 cups of shredded mozzarella and 3/4 cup of Parmesan cheese, distributing them evenly across the surface. For the best texture, I make sure the cheese topping is relatively even so it browns uniformly.
Cover the baking dish tightly with foil and bake for 25 minutes. Then carefully remove the foil and bake uncovered for another 10 minutes, until the cheese on top is melted and beginning to turn golden brown. The casserole is done when the sauce is bubbling gently around the edges and the top cheese is lightly browned.
Remove the casserole from the oven and let it rest for 5 minutes before serving—this allows the sauce to set slightly so it won't be overly runny when plated. Garnish generously with fresh chopped parsley and serve warm.