Preheat oven to 375 degrees Fahrenheit. Spray a 9 by 13 inch baking dish with cooking spray and set aside.
In a large bowl, whisk together the condensed soups, milk, salt, and pepper.
10.5 ounces cream of chicken soup, 10.5 ounces cream of mushroom soup, 1/2 cup milk, 1/4 teaspoon kosher salt, 1/4 teaspoon black pepper
Stir in the chicken. Then spread the mixture over the bottom of the prepared pan.
4 cups cooked, shredded chicken
Sprinkle the stuffing mix over the top of the chicken and soup mixture. Then pour the chicken broth over the top, ensuring that all of the stuffing mixture gets moistened.
6 ounces chicken stuffing mix, 1 1/2 cups chicken broth
Cover tightly with foil and bake for 35 minutes. Remove the foil and continue baking for 10 minutes or until the stuffing is lightly browned.