Prepare the chicken by shredding it into bite-sized pieces if using leftover chicken. If using raw chicken, cook it thoroughly before shredding.
In a large mixing bowl, combine the cooked, shredded chicken with the cream of chicken soup and chicken broth. Stir in the frozen mixed vegetables, garlic powder, onion powder, dried thyme, and black pepper. Mix well.
In another bowl, whisk together the milk, all-purpose flour, baking powder, and salt until smooth and pourable.
Grease a 9x13-inch baking dish. Spread the chicken and sauce mixture evenly across the bottom. Pour the dumpling batter over the chicken mixture and drizzle melted butter on top.
Preheat the oven to 350°F. Bake the casserole for 30-35 minutes until the top is golden brown and a toothpick inserted in the center comes out clean. Let it cool for 5 minutes before serving.