Preheat the oven to 375 degrees F. Spray an 8x8 baking dish with nonstick cooking spray.
Heat oil in a large skillet over medium heat. Cook the onions until softened, about 5 minutes. Add the minced garlic during the last 30 seconds.
Sprinkle flour over onions and cook 1 minute, stirring constantly. Slowly whisk in skim milk and chicken broth.
Stir in the seasonings and Dijon mustard. Simmer 4–5 minutes until thickened and creamy.
In a large bowl, combine the cooked chicken, cooked rice, spinach, 1/2 cup of mozzarella cheese, and Parmesan cheese. Pour the sauce over the mixture and stir until evenly coated.
Transfer to the prepared baking dish. Sprinkle the remaining 1/2 cup of mozzarella over the top.
Bake uncovered for 25–30 minutes, until bubbly and lightly golden on top.