In a small bowl, whisk together the soy sauce, oyster sauce, sesame oil, hoisin sauce, brown sugar, chicken broth, ginger, garlic, and cornstarch.
Bring a large pot of water to a boil and cook the egg noodles just until chewy and tender. Drain and rinse with cold water, then toss lightly with a drop of sesame oil.
Heat 1 tablespoon of vegetable oil in a hot wok. Add the chicken in a single layer and cook until golden, then flip and finish cooking. Remove and set aside.
Add remaining vegetable oil to the wok. Stir fry the onion, cabbage, bell pepper, carrots, and snow peas until crisp tender. Add the remaining garlic and ginger.
Return the chicken to the pan, add the cooked noodles, and pour in the lo mein sauce. Toss everything together over high heat until the noodles are evenly coated and glossy.
Remove from heat and garnish with green onions and sesame seeds. Serve immediately while warm.