In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion, carrots, and celery, sautéing until the vegetables are softened, about 5 minutes. Stir in the minced garlic and cook for an additional minute.
Pour in the gluten-free chicken broth and bring to a gentle boil. Add the chicken breasts, dried thyme, dried parsley, salt, and pepper. Reduce the heat to low, cover, and let it simmer for about 20 minutes or until the chicken is cooked through.
Once the chicken is cooked, remove it from the pot and shred it using two forks. Return the shredded chicken back to the pot and stir in the frozen peas.
In a mixing bowl, combine the gluten-free all-purpose flour, baking powder, salt, and garlic powder. Pour in the milk and melted butter, stirring until just combined. Do not overmix; the dough should be slightly lumpy.
Drop spoonfuls of the dumpling dough into the simmering broth. Cover the pot and let the dumplings cook for about 15 minutes without lifting the lid, allowing them to steam and rise.
Once the dumplings are cooked through, serve the chicken and dumplings hot, garnished with additional parsley if desired.