Heat the oil in a large saucepan set over medium-high heat. Add the ginger, garlic and half of the chiles. Cook and stir 30 seconds.
Add 2 cups of the broth. Cover. Bring to a boil. Reduce heat to medium low.
Add the chicken. Cook for 5 minutes or until just cooked through.
Using tongs, transfer the chicken to a cutting board. Slice crossways into strips.
Add the soy sauce, sesame oil, brown sugar, and the remaining 4 cups of broth. Cover. Increase the heat to medium-high. Bring to a boil.
Add the noodles. Cook 6 minutes, until noodles are tender.
Add the bok choy and cook 2 minutes longer, until bok choy is wilted.
Season with salt and pepper to taste.
Serve the soup topped with the sliced chicken, green onions, and remaining chiles.