Heat oven to 350 degrees. Lightly coat a 3-4 quart baking dish with cooking spray. Set aside.
Place cooked pasta and chicken in a large bowl. Set aside.
Melt butter in a large skillet over medium heat. Add garlic and cook for 15 seconds. Whisk in flour and cook for 1 minute. Add in milk, cream, nutmeg, and pepper.
Add Parmesan cheese and half of the mozzarella. Stir until cheese has melted and sauce is thickened. Taste and adjust seasoning with salt and pepper. Pour sauce over pasta and chicken. Mix well. Pour all ingredients into the prepared baking dish. Top with remaining cheese. Bake for 20 minutes until cheese is golden on top.
Remove from the oven and let rest for 5 minutes. Serve.