Start by marinating the chicken. Cut the chicken thighs into bite-sized pieces and transfer to a bowl with the marinade ingredients. Set aside for 20 minutes while you prep the rest of the ingredients.
When you're ready to cook, heat the oil in a wok over low heat. Add the star anise, cinnamon stick, bay leaves, ginger, garlic, Sichuan peppercorns, chilies, and sugar. Cook this mixture for 2 minutes, making sure they don’t burn. Add the chicken and turn up the heat. Stir-fry until the chicken is seared.
Add the potatoes and carrots and stir-fry for a minute. Then add the dark soy sauce, light soy sauce, shaoxing wine, and 3 cups water. Bring to a boil and reduce the heat to medium. Cover the wok and cook for 15 minutes, until the potatoes are tender.
While the chicken is cooking, bring a pot of water to a boil. Follow the package instructions to cook the noodles. Drain.
Once the potatoes are cooked through, by now, there should be at least 1 1 1/2 cups of liquid in the wok so add more water if needed.To your wok, stir in the bell peppers. Cover and simmer for another 5 minutes. Taste the dish and season with salt to taste. Now transfer the noodles to a large plate, and cover with your chicken and vegetables. Sprinkle with scallions and serve immediately!
Note: If you want more sauce, add a little more water to the wok. If the sauce is too thin, just turn up the heat to reduce and thicken the sauce.