Begin by heating the cooking oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the chicken pieces, skin side down, and sear until they develop a deep golden crust on all sides. Once browned, transfer the chicken to a plate and set aside.

In the same pot, add the chopped onion, smashed garlic cloves, and sliced ginger. Sauté for 3 to 5 minutes, stirring often, until the aromatics are softened and release their fragrance.

Return the seared chicken to the pot and pour in the chicken broth or water with bouillon. Add the star anise, cinnamon stick, and Sichuan peppercorns if using. Bring everything to a vigorous boil, then reduce the heat to low. Cover the pot and let the broth simmer gently for 30 to 40 minutes, or until the chicken is fully cooked and tender. Skim off any foam or impurities that float to the surface for a clearer broth.

Once the chicken is tender, stir in the soy sauce, Shaoxing wine, and sugar. Taste the broth and season with salt as needed. The resulting liquid should be aromatic, well-balanced, and deeply savory.

While the broth is finishing, prepare the noodles according to the package instructions. Once cooked, drain thoroughly. To keep them from sticking, rinse under cold water and set aside. Before serving, warm them briefly by dipping into hot water.

To serve, divide the noodles evenly among four serving bowls. Ladle the steaming hot broth and generous portions of chicken over the noodles. Top each bowl with halved hard-boiled eggs, a sprinkle of chopped green onions, and fresh cilantro. Offer chili oil at the table for those who enjoy an extra layer of heat and complexity. Serve piping hot.