Preheat the oven to 350°F.
Add the dry stuffing mix to a large bowl.
Pour the melted butter over the stuffing and stir as evenly as possible. Some pieces will absorb more butter than others.
Pour in the chicken broth and mix until all of the stuffing has been moistened.
Spread the chopped rotisserie chicken evenly across the bottom of a 9x13-inch baking dish.
In a separate bowl, whisk together the cream of chicken soup, cream of mushroom soup, and milk until smooth.
Pour the creamy soup mixture over the chicken and stir until the chicken is evenly coated.
Spread the moistened stuffing mixture evenly across the top.
Cover the baking dish with foil and bake for 30 minutes.
Carefully remove the foil and continue baking uncovered for 15–25 minutes, or until the stuffing topping is browned to your liking.
Remove the casserole from the oven and allow it to cool slightly before serving.