Spray a 3-quart baking dish with cooking spray, and preheat the oven to 350 F.
Cook the pasta until al dente according to package instructions, drain, and keep warm.
While the pasta is cooking, make the sauce: melt the butter in a large pan and saute the garlic. Add the flour and cook until slightly golden brown. Whisk in the milk and cream until no lumps remain, and cook until thickened. Stir in the Parmesan cheese, ½ cup mozzarella cheese, oregano, parsley, red pepper flakes, salt, and pepper until the cheeses are melted.
Add the cooked pasta and diced chicken, and mix until well combined. Pour into the prepared baking dish, top with the remaining mozzarella cheese, and bake, uncovered, for 20-25 minutes or until the cheese is melted and bubbly. Serve with freshly chopped parsley on top.