Prepare Chicken Stock: Combine 16 cups of water, chicken breast, garlic cloves, and a medium onion in a large pot. Boil for one hour over high heat.
Make Noodle Dough: In a bowl, mix 3.5 cups of all-purpose flour, 0.5 cup of starch, 1 teaspoon of salt, 2 tablespoons of cooking oil, and 1.25 cups of water. Stir with a wooden spoon to form a lump, then knead by hand for about 2 minutes until smooth. Let the dough rest.
Prepare Vegetables: Cut zucchini into matchsticks and mix with a quarter teaspoon of salt. Chop green onions. Sauté zucchini with a bit of sesame oil for flavor.
Make Spicy Sauce (Optional): Mix 1-2 tablespoons of hot pepper flakes with 2 teaspoons of sesame oil for a spicy version of the soup.
Season Chicken Stock: Remove chicken and vegetables from the stock. Add 1 tablespoon of salt, 2 teaspoons of fish sauce, mashed garlic from the stock, 1 teaspoon of salt, 2 teaspoons of sesame oil, and a quarter teaspoon of ground black pepper to the stock.
Prepare Noodles: Roll out the dough and cut into noodles. Boil noodles in the chicken stock until cooked.
Assemble Soup: Shred the cooked chicken and add back to the soup with the noodles. Serve hot with sautéed zucchini and green onions on top.