01 - Preheat oven to 375°F. Lightly grease a 9x13-inch baking dish.
02 - In a large skillet over medium heat, melt 2 tablespoons butter. Sauté onion, celery, and garlic until softened, about 4 minutes.
03 - Add chicken, peas and carrots, cream of chicken soup, chicken broth, milk, dried thyme, salt, and pepper to the skillet. Stir thoroughly and simmer for 3 minutes.
04 - Evenly spread the chicken mixture into the prepared baking dish.
05 - In a medium bowl, whisk together flour, baking powder, and salt.
06 - In a separate bowl, mix milk, melted butter, and beaten egg. Pour wet ingredients into dry ingredients and stir until just combined. Add chopped parsley if desired.
07 - Drop spoonfuls of the dumpling batter evenly over the chicken filling.
08 - Bake uncovered for 35 to 40 minutes until dumpling topping is golden and filling is bubbling.
09 - Allow casserole to rest for 10 minutes before portioning and serving.