Preheat the oven to 375°F (190°C).
Drizzle the melted butter into the base of a 9x13-inch baking dish, ensuring it's evenly spread.
Layer the cooked chicken over the butter, followed by an even distribution of the frozen mixed vegetables on top.
In a mixing bowl, whisk together the Cheddar Bay Biscuit mix (including the seasoning packet) and milk until the consistency is mostly smooth. A few small lumps are perfectly fine. Pour this mixture evenly over the vegetables.
In the same bowl, whisk together the chicken broth and the cream of chicken soup until well combined. Pour this blend over the biscuit layer.
Place the dish in the oven and bake for about 1 hour or until the top becomes golden and the center is just about set but still slightly jiggly. Avoid over-baking to retain a generous amount of gravy.
Let the cobbler rest for 10-15 minutes before serving to allow it to set and for flavors to meld.