In a large bowl, whisk together arrowroot powder, salt, and pepper. Dredge the chicken pieces in the mixture, coating them on all sides.
In a large, heavy-bottomed pan, heat the ghee. When hot, add the chicken in batches and cook until golden brown on all sides, 4-5 minutes a side.
Remove the chicken and set aside. Add the onion, celery, and carrots to the pot and sauté for 5-7 minutes, until the veggies have softened.
Stir the thyme and turmeric into the vegetables. Pour in the broth, scraping up any brown bits that are stuck to the bottom of the pot.
Return the chicken to the pot and bring to a simmer. Simmer the soup until the chicken is cooked through, about 20 minutes. Remove the chicken pieces and set them aside to cool.
While the soup is simmering, make the dumplings. Mix together the almond flour, cassava flour, baking soda, salt, and coconut milk. Use your hands to form the dough into 24 small dumplings. The dumplings should be somewhat round, but still rustic looking.
Drop the dumplings into the simmering soup and cook for 5 minutes.
When the chicken is cool enough to handle, remove the meat from the bones and shred it. Discard the skin and bones. (Save the bones for making broth, if desired.)
Add the shredded chicken and coconut milk to the soup and simmer another 3-4 minutes, until heated though. Garnish with fresh parsley or chives, if desired.