In a large pot, melt the ghee over medium heat and sauté the onion, carrots, and celery until the onions are translucent.
Add the chicken breast, sea salt, black pepper, and dried thyme, then pour in the chicken broth.
Bring the mixture to a gentle boil, then reduce heat to low and simmer for 15 minutes until the chicken is tender.
Remove the chicken from the pot, shred it into bite-sized pieces using two forks, and return it to the broth.
In a small mixing bowl, whisk the egg and then stir in the whole wheat flour, baking powder, and fresh parsley to create a thick dumpling batter.
Using a small spoon, drop rounded portions of the batter into the simmering broth, ensuring they do not overlap.
Cover the pot tightly and steam the dumplings for 8 minutes until they are puffed and cooked through.