Heat the olive oil in a medium pot over medium heat and sauté the onion, carrots, and celery until the onion is translucent and fragrant.
Cut the chicken breast into bite-sized pieces and add them to the pot, searing briefly for 2 minutes.
Pour in the chicken bone broth and add the dried thyme, sea salt, and black pepper, then bring the mixture to a gentle simmer.
In a small bowl, whisk together the whole wheat flour, baking powder, and chopped fresh parsley.
Add the water to the flour mixture and stir until a thick, sticky dough forms.
Using a small spoon, drop rounded tablespoons of the dough into the simmering broth, ensuring they are spaced apart.
Cover the pot with a tight-fitting lid and simmer for 10-12 minutes without lifting the lid to allow the dumplings to steam and fluff up.
Remove the lid, gently stir in the frozen peas, and cook for 1 more minute until the peas are bright green and the broth has thickened slightly.
Ladle the chicken and dumplings into a bowl and serve immediately while hot.