Preheat the oven to 350°F and grease a 9x13-inch baking dish.
In a large bowl, stir together the shredded chicken, cream of chicken soup, sour cream, chicken broth, salt, and pepper. Fold in the peas and carrots if using.
Spread the chicken mixture evenly into the prepared baking dish.
In a separate bowl, toss the dry stuffing mix with the melted butter until fully coated.
Sprinkle the buttered stuffing mix evenly over the chicken layer, covering it completely.
Bake uncovered for 35–40 minutes, until the topping is deep golden brown and the filling is bubbling at the edges.
Let rest for 10 minutes before serving.