Using a large Dutch oven, heat the ghee over medium heat. Add the carrots, onion, and celery and saute until tender, about 5-6 minutes. Add the garlic at the end and saute for another minute.
Lightly season with salt and pepper, and add the flour to the pot, tossing to coat the vegetables.
Begin adding the broth just a splash at a time, scraping the bottom of the pan with a wooden spoon as you go to remove stuck bits. Add the remainder of the broth and the coconut milk. Add the chicken, peas, sage and thyme. Stir well and begin to bring to a low boil.
While you wait for the soup to come up to a low boil, prepare the dumpling dough by combining the ghee, eggs, milk, broth, and apple cider vinegar in a bowl. Combine the two flours, baking powder, salt, and parsley in a separate bowl and whisk well. Add the dry ingredients to the wet ingredients and stir well to combine. You should have a sticky dough.
Once the soup is boiling, use an ice cream scoop to scoop large dumplings into the soup. You should have 10-12, depending on the size of your scoop. Spoon a bit of broth over each dumpling. Reduce the soup down to a medium simmer and cover the pot tightly to allow the dumplings to steam. Simmer for 18-20 minutes or until the dumplings float and are cooked through.
Serve topped with additional thyme!