In a large pot or Dutch oven, combine the chicken broth, diced carrots, diced celery, chopped onion, minced garlic, dried thyme, dried parsley, black pepper, and salt. Bring the mixture to a simmer over medium heat.
Add the chicken breasts to the pot and cook for about 15-20 minutes, or until fully cooked and tender. Remove the chicken from the pot and set aside to cool.
While the chicken cools, prepare the dumpling mixture. In a mixing bowl, combine the all-purpose flour, baking powder, and ½ teaspoon salt. In another bowl, whisk together the milk and egg. Gradually add the wet ingredients to the dry ingredients, mixing until just combined. Do not overmix.
Shred or chop the cooked chicken into bite-sized pieces and return it to the pot with the broth and vegetables.
Drop spoonfuls of the dumpling mixture onto the simmering soup. Make sure they are spaced apart, as they will expand while cooking.
Cover the pot and let the dumplings cook for 10-12 minutes, or until they are fluffy and cooked through. Avoid lifting the lid during this time to ensure the dumplings steam properly.
Once the dumplings are ready, taste the soup and adjust the seasoning if needed. Serve hot with a ladle, and enjoy!