Heat the oven. Preheat to 400°F (200°C).
Grease a 9x13-inch baking dish with 1 tablespoon of the melted butter or cooking spray.
Make the filling. In a large bowl, whisk together the cream of chicken soup, chicken broth (or milk), garlic powder, onion powder, thyme, and a pinch of salt and pepper until smooth.
Layer the dish. Spread the frozen mixed vegetables in an even layer in the baking dish. Add the chicken on top. Pour the soup mixture evenly over everything and gently nudge with a spatula to let it seep down.
Do not stir aggressively; just level it out.
Whisk the topping. In a medium bowl, whisk the flour, baking powder, and salt. Stir in the milk and 2 tablespoons melted butter until just combined. You want a thick, pourable batter.
Avoid overmixing.
Add the batter. Pour the batter evenly over the filling. It won’t fully cover; it spreads while baking. Drizzle the remaining 1 tablespoon melted butter on top.
If using cheese, sprinkle it over now.
Bake. Bake for 30–35 minutes, until the topping is puffed and deep golden brown and the filling is bubbling around the edges. If the top is browning too fast, tent loosely with foil for the last 10 minutes.
Rest and serve. Let the bake rest for 10 minutes so the filling thickens slightly. Taste and finish with a pinch of salt and pepper if needed.
Serve warm.