In a large pot, add the chicken pieces and cover with chicken broth. Bring to a boil, then reduce heat and simmer for about 45 minutes, until the chicken is cooked through.

Remove the chicken from the pot and shred the meat using two forks. Discard the bones and skin. Set the shredded chicken aside.

In a mixing bowl, combine the flour, baking powder, and salt. Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs. Stir in the milk until a soft dough forms.

Drop the dough by spoonfuls into the simmering broth. Cover and cook for 10 minutes, or until the dumplings are cooked through.

In the same pot, add the diced carrots, celery, onion, and garlic to the broth. Season with salt and pepper to taste. Simmer for another 15-20 minutes, until the vegetables are tender.

Return the shredded chicken to the pot and stir to combine. Ladle the soup into bowls and garnish with fresh parsley.