Preheat the oven to 375°F (190°C).
Pour melted butter into a greased baking dish to coat the bottom.
In a bowl, combine frozen peas and carrots with chopped celery and onions.
Layer shredded chicken in the baking dish followed by the vegetable mixture.
In another bowl, mix biscuit mix, milk, and half of the shredded cheddar cheese until well combined.
Whisk together chicken broth and cream of chicken soup, then pour over the vegetable layer without stirring.
Spread the biscuit mixture evenly over the creamy chicken and vegetable layer.
Bake for 45 minutes to 1 hour, until the topping is golden brown and bubbling.
Allow to cool slightly before serving.