Heat the oil in a large pot over medium heat. Add the chicken breast and sauté until browned on both sides, about 5-7 minutes per side.
In the same pot, add the water, ginger, scallions, onion, and garlic. Bring to a simmer over medium heat. Reduce the heat to low, cover, and let simmer for 90 minutes.
After 90 minutes, remove the chicken breast from the pot and set aside to cool slightly. Strain the broth through a fine mesh sieve or cheesecloth to remove the ginger, scallion, onion, and garlic. Return the strained broth to the pot.
Season the broth with the flavor packets from the ramen noodles and soy sauce. Stir well to combine.
Shred the chicken breast using two forks or your fingers and add them back to the pot.
Add the mushrooms and bok choy to the pot and bring the broth back to a simmer. Let it cook for another 10 minutes.
Once the mushrooms are tender, add the ramen noodles to the pot and cook for 2 more minutes. Stir well to combine.
Taste the soup and adjust the seasoning with salt and pepper if necessary.
Serve the Asian Chicken Soup hot, garnished with additional chopped scallions if desired.