Preheat the oven to 350°F.
Add 4 tablespoons butter to a 9x13-inch baking dish and place it in the oven until the butter has melted.
While the butter melts, remove the meat from the rotisserie chicken and chop it into bite-size pieces.
In a bowl, whisk together the cream of chicken soup and chicken broth until smooth.
In a separate bowl, combine the Cheddar Bay biscuit mix, garlic powder, onion powder, dried parsley, and milk. Set the included seasoning packet aside.
Carefully remove the baking dish from the oven. Spread the chopped chicken evenly over the melted butter.
Layer the frozen mixed vegetables over the chicken.
Pour the cream of chicken mixture evenly over the vegetables.
Pour the biscuit mixture evenly over the top. Do not stir the layers together. The casserole will look very soupy at this stage.
Bake uncovered for 50–60 minutes, or until the topping is golden brown and the center has very little jiggle.
Melt the remaining 2 tablespoons butter and mix it with the reserved Cheddar Bay seasoning packet.
Brush the seasoned butter over the hot biscuit topping.
Allow the Chicken Cobbler to rest for 15–20 minutes before serving so the filling can finish setting.