In a large pot, melt the butter over medium heat. Add the chopped onion, carrots, and celery. Sauté for about 5 minutes until the vegetables are tender.

Stir in the shredded chicken, chicken broth, garlic powder, thyme, salt, and black pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 10 minutes.

In a separate bowl, whisk together 1/4 cup flour and 1/2 cup milk until smooth. Gradually add this mixture to the pot, stirring constantly until the broth thickens slightly.

In another bowl, combine 1 1/2 cups flour, baking powder, and 1/2 teaspoon salt. Stir in 1/2 cup milk until a soft dough forms.

Drop spoonfuls of the dumpling dough into the simmering chicken mixture. Cover the pot and let the dumplings cook for about 15 minutes without lifting the lid.

Once the dumplings are cooked through, serve the chicken and dumplings hot, garnished with fresh parsley if desired.