Dice the chicken breast into bite-sized pieces and season lightly with salt and pepper if desired.
Chop the carrot, celery, and onion into uniform pieces.
In a medium pot, heat a splash of water or a light cooking spray over medium heat, then add the onions, carrots, and celery. Sauté until they begin to soften, about 5 minutes.
Add the chicken pieces to the pot and cook until lightly browned on all sides.
Pour in the low sodium chicken broth, bring the mixture to a simmer, and let it cook for about 10 minutes, allowing flavors to meld.
While the stew simmers, prepare the herb dumplings by combining the whole wheat flour, egg white, and fresh mixed herbs in a small bowl. Stir until a soft dough forms; it should be slightly sticky but hold together.
Using a spoon, gently drop small dumpling portions into the simmering stew, covering the surface evenly.
Cover the pot and let it simmer for an additional 8-10 minutes until the dumplings are fluffy and fully cooked.
Taste and adjust seasoning as needed, then serve hot.