First, preheat your oven to 350ºF and lightly spray your baking dish with cooking spray. In a skillet, melt butter over medium-high heat. Add onion, celery, and carrots, cooking until tender, about 3–5 minutes.
Sprinkle flour over the vegetables and whisk to combine. Gradually pour in chicken broth and half and half, stirring constantly until the sauce thickens. Add shredded chicken, garlic powder, parsley, basil, salt, and pepper, mixing thoroughly.
Pour the chicken-vegetable mixture into your prepared baking dish. Prepare the dumplings by cutting cold butter into flour, baking powder, salt, and parsley. Stir in milk until dough forms and drop spoonfuls evenly over the casserole. Cover loosely with foil and bake 30 minutes, then uncover and bake 10–15 minutes until dumplings are lightly browned.