Preheat the oven to 350°F (175°C). Place the 9×9-inch baking dish in the oven while it preheats.
Put the butter in the hot baking dish and allow it to melt completely in the oven, then carefully remove the dish.
In a mixing bowl, whisk together the flour, baking powder, salt, milk, and taco seasoning until smooth to make the batter.
Pour the batter over the melted butter in the baking dish, tilting the dish so the batter forms a ring around the edges and leaves the center open.
In another bowl, combine the chopped cooked chicken, cooked Mexican or Spanish rice, chicken broth, and black pepper; stir until evenly mixed.
Spoon the chicken-and-rice mixture into the center of the baking dish so it fills the middle and the batter remains around the perimeter.
Bake for 50 minutes to 1 hour, until the cobbler topping is golden brown and set.
Let the dish rest for about 5 minutes before serving.