First, preheat your oven to 350°F and lightly grease a casserole dish with non-stick spray. In a large skillet over medium-high heat, melt the butter. Add the minced onion, chopped celery, and chopped carrots, and cook until they become tender, which should take about 3 to 5 minutes.
Sprinkle the all-purpose flour over the cooked vegetables and whisk it in to form a paste. Slowly pour in the chicken broth and half-and-half, whisking continuously to prevent lumps and create a smooth gravy. The mixture will begin to thicken as you whisk.
Next, stir in the cooked chicken, garlic powder, dried parsley, and dried basil. Season with salt and pepper to your liking and let everything cook together for a few more minutes. Pour the entire mixture from the skillet into your prepared casserole dish, spreading it out evenly.
In a separate mixing bowl, combine the flour, baking powder, salt, and dried parsley for the dumplings. Use a pastry blender or a fork to cut the cold, cubed butter into the flour mixture until it resembles coarse crumbs. Pour in the whole milk and stir just until the dough comes together; be careful not to overmix.
Drop spoonfuls of the dumpling dough evenly over the top of the chicken filling in the casserole dish. Cover the dish loosely with aluminum foil, making sure the foil doesn't touch the dumplings. Bake for 30 minutes, then remove the foil and bake for another 10-15 minutes, or until the dumplings are golden brown and cooked through. Let it cool for a few minutes before serving.