Melt the butter in a large pot over medium heat. Add the onion, carrots, and celery. Cook for 5 minutes until the vegetables soften slightly.
Add the chicken pieces to the pot. Stir and cook for 4 minutes until the chicken is no longer pink on the outside.
Pour in the chicken broth. Add the thyme, salt, and pepper. Bring the mixture to a simmer and cook for 10 minutes.
In a mixing bowl, stir together the flour, baking powder, and milk until a thick batter forms. Do not overmix.
Drop spoonfuls of the batter directly into the simmering broth. Cover the pot and cook for 12 minutes without lifting the lid.
Remove the pot from the heat. Sprinkle the parsley over the top before serving.