Heat the neutral oil in a large pot or Dutch oven over medium heat.
Add the ginger, garlic, and the white parts of the green onions. Sauté for 2-3 minutes until fragrant and slightly softened, being careful not to burn the garlic.
Pour in the chicken broth and soy sauce. Bring the mixture to a boil, then reduce the heat to a gentle simmer.
Add the whole chicken thighs or breasts to the pot. Cover and simmer for 15-20 minutes, or until the chicken is fully cooked and tender (internal temperature reaches 165°F).
Remove the chicken from the pot and transfer to a cutting board. Use two forks to shred the meat into bite-sized pieces.
Return the shredded chicken to the simmering broth. Add the prepared baby bok choy.
Simmer for 3-5 minutes until the bok choy is tender but still retains a slight crunch in the stems.
Stir in the toasted sesame oil and red chili flakes.
Ladle into bowls and garnish generously with the reserved green onion tops before serving.