In a large pot, heat the olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté until the vegetables are softened, about 5-7 minutes.
Stir in the minced garlic, thyme, and rosemary, cooking for an additional minute until fragrant.
Add the chicken breasts to the pot, followed by the chicken broth. Bring the mixture to a simmer. Cover and cook for about 15-20 minutes, or until the chicken is fully cooked.
While the chicken is cooking, prepare the dumplings. In a mixing bowl, whisk together the gluten-free flour, baking powder, and salt. Stir in the milk and melted butter until just combined. Do not overmix.
Once the chicken is cooked, remove it from the pot and shred it with two forks. Return the shredded chicken to the pot, along with the frozen peas. Season with salt and pepper to taste.
Using a spoon, drop dollops of the dumpling batter onto the simmering broth, making about 12 spoonfuls. Cover the pot with a lid and let the dumplings steam for about 15 minutes, or until they are puffed and cooked through.
Serve the chicken and dumplings hot, garnished with fresh parsley.
For a creamier broth, you can stir in a splash of heavy cream after adding the peas.
If you prefer, you can substitute the chicken breasts with chicken thighs for more flavor.
Ensure all ingredients used, particularly the chicken broth and gluten-free flour, are certified gluten-free to avoid cross-contamination.