Melt the butter in a large pot over medium heat.
Add the chicken and cook for 5 to 6 minutes until lightly browned. Transfer to a plate.
Add the onion, carrots, and celery to the pot. Cook for 4 to 5 minutes until softened.
Stir in the garlic and cook for 30 seconds until fragrant.
Pour in the chicken broth and add the thyme, parsley, salt, and black pepper. Bring to a boil.
Return the chicken to the pot, reduce the heat to a simmer, and cook for 10 minutes.
In a medium bowl, whisk together the flour, baking powder, and salt. Stir in the melted butter and milk until just combined. Do not overmix.
Drop tablespoon-sized portions of the dumpling dough onto the simmering soup.
Cover the pot with a tight-fitting lid and cook for 15 minutes without lifting the lid.
Sprinkle with fresh parsley and serve hot.