In a large pot over medium heat, combine the chicken broth, carrots, celery, onion, garlic powder, thyme, salt, and black pepper. Bring to a simmer and cook for about 10 minutes, until the vegetables are tender.
Stir in the shredded chicken and frozen peas, and let it simmer for another 5 minutes.
In a separate bowl, mix together the flour, baking powder, and salt. Add the melted butter and 3/4 cup of milk, stirring until just combined to form a dough.
Drop spoonfuls of the dumpling mixture into the simmering chicken mixture. Cover the pot and let the dumplings cook for about 15 minutes without lifting the lid.
After 15 minutes, check the dumplings for doneness; they should be fluffy and cooked through. Serve hot.