Pat the chicken dry with a paper towel. Thoroughly preheat a Dutch Oven or thick-bottomed soup pot over medium-high heat. Reduce the heat to medium, add the oil, and then add the chicken leg quarters skin-side down. Cook for 3-4 minutes, until lightly browned, and then flip and cook on the other side for 3-4 minutes.
Add the Shaoxing wine, water, ginger slices, and whole scallion (you can cut it in half crosswise to fit into the pot). Cover and bring to a boil. Once boiling, immediately reduce the heat to the medium-low, and simmer (covered tightly) for 40 minutes.
Bring a separate pot of water to a boil for the noodles. Remove the chicken leg quarters from the soup pot, and let cool for a few minutes. Add salt and white pepper powder to the soup to taste. Cover and keep warm on the stove. Shred the chicken into large strips with a fork.
By now, your water should be boiling. Cook the noodles according to package instructions. In the last 30 seconds to 1 minute of cooking, add the leafy greens, and cook along with the noodles.
Divide the noodles and greens among 2-3 bowls, and ladle the soup broth on top. Top with the shredded chicken and chili oil (if desired). Serve!