Bring a large pot of water to a boil. Add the lo mein noodles and cook according to package instructions until al dente, about 4-5 minutes. Drain and rinse under cold water. Set aside.
In a small bowl, whisk together soy sauce, oyster sauce, hoisin sauce, sesame oil, and chicken broth. Set the sauce mixture aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced chicken and cook, stirring frequently, until the chicken is cooked through and no longer pink, about 4-5 minutes. Remove chicken from the skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet. Add minced garlic and ginger and sauté for 30 seconds until fragrant.
Add the sliced onion, carrot, snow peas, mushrooms, and shredded cabbage to the skillet. Stir-fry the vegetables until tender-crisp, about 3-4 minutes.
Return the cooked chicken to the skillet with the vegetables. Pour the prepared sauce over the mixture and stir to combine.
Add the cooked noodles to the skillet and toss everything together until the noodles are evenly coated with the sauce and heated through, about 2 minutes.
Remove from heat and garnish with sliced green onions. Serve immediately.