Cook the lo mein noodles according to package instructions until al dente. Drain and rinse under cold water. Set aside.
In a small bowl, whisk together soy sauce, oyster sauce, hoisin sauce, chicken broth, cornstarch, sesame oil, and white pepper. Set the sauce mixture aside.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced chicken to the skillet and stir-fry until cooked through and lightly browned, about 5-6 minutes. Remove the chicken from the skillet and set aside.
Add the remaining 1 tablespoon vegetable oil to the skillet.
Add the minced garlic and ginger, and stir-fry for 30 seconds until fragrant.
Add the carrot, snow peas, shiitake mushrooms, and napa cabbage to the skillet. Stir-fry for 3-4 minutes until the vegetables are crisp-tender.
Return the cooked chicken to the skillet and add the cooked noodles.
Pour the prepared sauce over the noodles and stir well to combine all ingredients.
Continue to cook and toss for 2-3 minutes until the sauce thickens and everything is heated through.
Remove from heat and garnish with sliced green onions before serving.