Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with a little of the unsalted butter to prevent sticking.

Spread the cooked shredded chicken evenly over the bottom of the prepared baking dish, breaking up any large clumps.

Scatter the frozen mixed vegetables evenly over the chicken, keeping them in a single layer as much as possible.

In a medium saucepan over medium heat, add the remaining unsalted butter, chicken broth, and condensed cream of chicken soup. Stir until the mixture is smooth and warmed through, about 3 to 4 minutes.

Stir the garlic powder, onion powder, dried thyme, dried oregano, salt, and black pepper into the warm soup mixture until well combined.

Pour the seasoned soup mixture evenly over the chicken and vegetables in the baking dish, gently tilting the dish if needed so everything is lightly coated.

In a mixing bowl, whisk together the all-purpose flour, baking powder, granulated sugar, and salt for topping until there are no lumps of flour.

Add the milk and melted unsalted butter to the dry ingredients and stir just until a thick but pourable batter forms. Do not overmix; a few small lumps are fine.

Spoon or pour the batter evenly over the chicken and vegetable mixture, spreading it gently with the back of a spoon to cover most of the surface.

Place the baking dish on the middle rack of the preheated oven and bake for 35 to 40 minutes, or until the topping is golden brown and cooked through and the filling is bubbling around the edges.

Remove the Chicken Cobbler Casserole from the oven and let it rest for 10 minutes so the filling can thicken slightly before serving.

Scoop the casserole into bowls or onto plates, making sure each serving includes some of the chicken, vegetables, and biscuit-style topping.