Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan with cooking spray.
Spread rice in the bottom of the baking pan. Layer chicken on top.
Mix cream of chicken soup, milk, and cheese wedges together in a bowl until smooth. Stir in chicken broth and pesto. Pour over chicken and rice. Cover baking pan tightly with aluminum foil.
Bake in the preheated oven until most of the liquid has been absorbed, about 45 minutes. Remove from oven carefully; stir. Replace aluminum foil cover. Continue baking until rice is tender, about 15 minutes more. Remove from oven; uncover and sprinkle Parmesan cheese on top.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Broil until Parmesan cheese is melted and browned, about 5 minutes.
