In a large pot, combine the chicken pieces and 12 cups of water. Bring to a boil over high heat.
Once boiling, reduce heat to medium-low and skim off any foam or impurities that rise to the surface.
Add the onion halves, garlic cloves, and sliced ginger to the pot. Simmer uncovered for 30 minutes to create a flavorful broth.
After 30 minutes, remove the chicken pieces from the broth and set aside to cool slightly.
Strain the broth through a fine mesh sieve into another large pot to remove solids. Discard the solids and return the clear broth to the pot.
When the chicken is cool enough to handle, shred the meat into bite-sized pieces, discarding bones and skin.
Add the shredded chicken back into the broth along with the sliced carrots, zucchini, chopped green onions, kosher salt, black pepper, and soy sauce.
Bring the soup back to a gentle simmer and cook for 10 minutes until the vegetables are tender.
While the soup simmers, prepare the noodles: if using fresh wheat noodles, separate them gently to prevent sticking.
In a small pan, heat the vegetable oil over medium heat and quickly scramble the beaten egg until just cooked. Remove from heat and set aside.
Add the fresh noodles to the simmering soup and cook for 3 to 4 minutes until the noodles are tender but still chewy.
Turn off the heat and stir in the toasted sesame oil and scrambled egg pieces.
Ladle the soup into bowls and garnish each serving with toasted sesame seeds and chopped fresh cilantro if desired.
Serve hot and enjoy your authentic Korean chicken noodle soup!