Heat the olive oil in a medium pot over medium heat and sauté the onion, carrots, and celery until they begin to soften.
Add the chicken breast and chicken broth to the pot, bringing the liquid to a gentle simmer.
Season the broth with sea salt and black pepper, then cover the pot and cook for 10 minutes until the chicken is cooked through.
Remove the chicken from the pot, shred it into bite-sized pieces using two forks, and return the meat to the simmering broth.
In a small mixing bowl, whisk together the all-purpose flour, baking powder, and chopped fresh parsley.
Stir in the skim milk slowly until a thick, tacky dough forms.
Drop small spoonfuls of the dumpling dough directly onto the surface of the simmering broth.
Cover the pot tightly with a lid and steam for 10 minutes without lifting the cover until the dumplings are fluffy and cooked through.