Heat a large pot over medium heat. Add the chicken pieces and season with salt and pepper. Cook until lightly browned on all sides.
Add the onion, carrots, celery, and thyme to the pot. Stir and cook for 5 minutes until the vegetables begin to soften.
Pour in the chicken broth and bring the mixture to a simmer. Let it cook for 10 minutes.
While the stew simmers, stir together the flour, baking powder, and 1/2 teaspoon salt in a bowl. Add the milk and melted butter, mixing just until a thick dough forms.
Drop spoonfuls of the dumpling dough directly onto the surface of the simmering stew. Cover the pot and cook for 12 minutes without lifting the lid.
Remove the pot from the heat. Sprinkle with chopped parsley before serving.