Whisk the soy sauce, oyster sauce, hoisin sauce, sesame oil, brown sugar, water or broth, cornstarch if using, and red pepper flakes if using in a bowl until combined.

Boil the lo mein noodles according to the package directions, usually about 4–6 minutes. Cook them until just tender, drain, rinse briefly under cold water if very starchy, and toss with a small amount of oil to prevent sticking.

Season the sliced chicken with kosher salt and black pepper. Heat 1 tablespoon oil in a large wok or skillet over medium-high to high heat, then stir-fry the chicken for about 4–6 minutes, until browned and cooked through. Transfer it to a plate.

Add the remaining 1 tablespoon oil to the pan. Stir-fry the broccoli, carrots, and bell pepper for 3–4 minutes, then add the snow peas, garlic, and ginger and cook for 1–2 minutes more.

Return the chicken to the pan and add the cooked noodles and sauce. Toss continuously for 2–3 minutes, until the noodles are hot, evenly coated, and the sauce has lightly thickened.

Stir in the sliced green onions and serve immediately while the noodles are glossy and hot.