Season the chicken with a sprinkle of sea salt and black pepper.
Heat the olive oil in a large and heavy pot and sear the chicken until the chicken gets some color, about 4 minutes. Transfer the chicken to a plate and let cool for a few minutes. Cut the chicken into bite-size.
In the same pot, cook the onion, carrots, and celery until the onions are translucent. Return the chicken to the pot and pour in the chicken stock and water. Add the bay leaves and bring to a boil. Lower the heat to a simmer, cover, and cook for 25 minutes.
Check the seasoning and season with sea salt and black pepper to taste. Add the dried egg white noodles and cook until the noodles are tender.
Stir in the soy sauce, brown sugar, and green onions and simmer for another minute. Remove the bay leaves and serve hot.