Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.
In a large mixing bowl, combine the condensed cream of chicken soup, sour cream, and black pepper, whisking until smooth.
Fold the shredded rotisserie chicken and frozen peas and carrots into the cream mixture until the protein is evenly coated.
Transfer the chicken mixture to the prepared baking dish and spread it into an even layer.
In a separate bowl, toss the dry stuffing mix with the chicken broth and melted butter until the crumbs are uniformly moistened.
Distribute the stuffing mixture evenly over the top of the chicken base.
Bake for 30 minutes or until the internal liquid is bubbling and the stuffing topping has reached a golden brown color.
Allow the casserole to rest for 5 minutes at room temperature before serving to allow the sauce to set.