Heat the olive oil in a medium pot over medium heat and sauté the diced onion, carrots, and celery until they are softened and fragrant.
Add the whole chicken breast and the chicken bone broth to the pot, bringing the liquid to a gentle simmer.
Cook until the chicken is opaque and cooked through, then remove the chicken from the pot and shred it into bite-sized pieces using two forks.
Return the shredded chicken to the simmering broth and season with sea salt and black pepper.
In a small mixing bowl, whisk together the almond flour, tapioca starch, egg white, and dried thyme until a thick, uniform batter forms.
Using a small spoon, carefully drop rounded tablespoons of the batter into the simmering broth.
Cover the pot with a tight-fitting lid and let the dumplings steam for 5 to 7 minutes until they are firm and cooked through.
Ladle the soup and dumplings into a bowl and garnish with freshly chopped parsley before serving.