In a large pot, heat the chicken broth over medium heat. Add the chicken breasts, onion, carrots, celery, garlic, thyme, salt, and pepper. Simmer for about 20 minutes or until the chicken is fully cooked and tender. Remove the chicken, shred it, and return it to the pot.
In a mixing bowl, combine flour, baking powder, and salt. Cut in the butter using a pastry cutter or your hands until the mixture resembles coarse crumbs. Slowly add the milk and mix until a soft dough forms.
Bring the broth to a gentle boil. Drop spoonfuls of the dumpling dough into the pot, making sure they do not overcrowd. Reduce the heat to a simmer, cover, and cook for 15 minutes without lifting the lid to allow the dumplings to steam properly.
Gently stir the chicken and dumplings, allowing them to thicken slightly. Taste and adjust seasoning if needed. Serve warm with fresh parsley for garnish.