Preheat the oven to 350 degrees Fahrenheit. In a 9x13-inch baking dish, pour in the melted butter evenly into the bottom. You may need to tilt the baking dish a few ways to get it to spread out.
Sprinkle the shredded chicken evenly on top of the melted butter (do not stir.)
Then evenly sprinkle the frozen mixed vegetables on top of the chicken layer (do not stir).
In a separate bowl, whisk together cream of chicken soup, chicken broth, garlic powder, onion powder and black pepper. Whisk until well combined.
Pour this mixture over the chicken and mixed vegetables layers (do not stir.)
In the mixing bowl add the biscuit mix, seasoning packet that came with biscuit mix, milk and shredded cheese and stir until combined well.
Pour this biscuit mix layer as evenly as possible on top of the other layers in the baking dish (do not stir.)
Bake in preheated oven at 350 degrees Fahrenheit, uncovered, for about 50-60 minutes until bubbly and top is golden brown.
Allow the cobbler to rest for at least 10-15 minutes to thicken up. If you dig into it too soon after removing from the oven, it will be runny.