Heat the olive oil in a medium pot over medium heat and sauté the onion, carrots, and celery until they are softened and fragrant.
Add the chicken breast, chicken broth, dried thyme, sea salt, and black pepper to the pot, then bring the liquid to a gentle simmer.
While the soup base is simmering, whisk together the whole wheat flour, baking powder, and dried parsley in a small mixing bowl.
Stir the Greek yogurt and water into the flour mixture until a soft, slightly tacky dough forms, being careful not to overmix.
Once the chicken is cooked through, remove it from the pot, shred it into bite-sized pieces with two forks, and return it to the broth.
Drop small spoonfuls of the dumpling dough onto the surface of the simmering broth, cover the pot tightly, and steam for 10 minutes.
Ladle the hot chicken and broth into a bowl, ensuring each serving includes the pillowy, herb-flecked dumplings.