In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and garlic, sautéing until softened (about 3 minutes).
Add the sliced carrots and celery to the pot, cooking for another 5 minutes.
Pour in the chicken broth, and stir in the shredded chicken, frozen peas, thyme, rosemary, and season with salt and pepper. Bring to a gentle boil.
While the broth is heating, prepare the dumplings. In a mixing bowl, combine the gluten-free flour, baking powder, and salt. Stir in the milk and melted butter until just combined.
Once the broth is boiling, drop spoonfuls of the dumpling mixture on top of the simmering broth. Cover the pot and reduce heat to low.
Cook for 15-20 minutes without lifting the lid, until the dumplings have puffed up and are cooked through.
Serve hot, garnished with additional herbs if desired.