In a large pot, combine the chicken broth, carrots, celery, onion, garlic, thyme, parsley, salt, and pepper. Bring to a boil over medium-high heat.
Reduce heat and let simmer for about 10 minutes until the vegetables are tender.
In a mixing bowl, whisk together the flour, baking powder, and salt. Stir in the milk and melted butter until just combined. Do not overmix; the batter should be slightly lumpy.
Drop spoonfuls of the dumpling batter into the simmering broth. Cover the pot and let the dumplings cook for about 15 minutes without lifting the lid.
Stir in the shredded chicken and let it heat through for an additional 5 minutes. Adjust seasoning if necessary.