Cook the Noodles: Bring a large pot of water to a rolling boil and cook the lo mein noodles until just tender—al dente with a springy bite. Drain and toss with 1 tablespoon of avocado oil to prevent sticking. Set aside and keep warm.
Make the Sauce: In a small bowl or measuring cup, combine the oyster sauce, soy sauce, sesame oil, chicken broth, and cornstarch. Whisk until smooth and well blended. Set the sauce mixture aside for later use.
Sear the Chicken: In a large skillet or wok, heat 2 tablespoons of avocado oil over medium-high heat. Add the sliced chicken breast and stir-fry until golden and cooked through, about 2–3 minutes. Transfer the chicken to a plate and keep warm.
Sauté the Aromatics: Add the remaining tablespoon of oil to the pan. Stir in the minced garlic and chopped ginger, cooking for about 1 minute or until aromatic and slightly golden.
Stir-Fry the Vegetables: Add the shredded cabbage, sliced bell pepper, matchstick carrots, and the white parts of the green onions to the pan. Stir-fry for 2–3 minutes, just until the cabbage starts to soften and everything is crisp-tender.
Combine Sauce and Chicken: Return the cooked chicken to the skillet, pour in the prepared sauce, and stir everything together. Cook for another 2 minutes, allowing the sauce to thicken and coat the ingredients evenly.
Toss in Noodles and Serve: Add the cooked noodles to the skillet and toss gently with tongs until they’re fully coated in sauce and evenly mixed with the chicken and veggies. Sprinkle with the green parts of the scallions and serve hot.