In a medium stockpot, bring chicken stock to a simmer over medium heat. Add ginger, garlic, 1/4 cup each of the cilantro and mint leaves, and chicken. Simmer until chicken is cooked through, about 30 minutes.
Remove chicken and allow to cool. Tear each breast into about 6 pieces, discard bones. Strain broth and return to pot over low heat. Add bok choy and simmer 5–10 minutes.
Soak noodles in hot water until softened, 5–10 minutes. Cook noodles in boiling water until tender, about 3 minutes. Drain and rinse well with cold water.
Divide noodles among six bowls. Add chicken pieces, scallions, remaining 1/4 cup each mint and cilantro, and tatsoi. Pour hot broth and bok choy over top. Serve with Tuong Ot Toi.