Preheat your oven to 375°F (190°C). Place the butter directly into a 9×13-inch baking dish and let it melt in the oven while it preheats. Once melted, carefully remove the dish from the oven.

Spread the shredded cooked chicken evenly over the melted butter without stirring. Scatter the frozen mixed vegetables evenly over the chicken, creating a uniform layer. Sprinkle the garlic powder, onion powder, thyme, salt, and black pepper across the top.

In a large mixing bowl, whisk together the biscuit baking mix and milk until smooth. If using cheddar cheese, fold it into the batter. Carefully pour the batter evenly over the chicken and vegetables without stirring. The distinct layers help create the signature cobbler texture during baking.

In another bowl, whisk together the chicken broth and cream of chicken soup until completely smooth. Slowly pour the mixture over the biscuit batter, again avoiding stirring. The layers will naturally combine while baking to create a creamy filling beneath the fluffy topping.

Transfer the baking dish to the oven and bake for 40 to 45 minutes, or until the biscuit topping is beautifully golden brown and cooked through. The filling should be bubbling gently around the edges while the top becomes lightly crisp.

Remove the Chicken Cobbler from the oven and let it rest for 10 minutes before serving. This allows the creamy filling to thicken slightly, making it easier to scoop neat portions. Garnish with freshly chopped parsley and, if desired, an extra sprinkle of shredded cheddar cheese. Serve warm and enjoy the fluffy biscuit topping with the rich, creamy chicken filling.