In a small bowl, make the sauce by whisking together oyster sauce, soy sauce, 1 teaspoon sesame oil, and cornstarch until well combined. Stir in chicken broth, garlic, and ginger. Set aside.
Cook chow mein noodles according to package directions.
Meanwhile, heat 1 tablespoon sesame oil in a large skillet over medium high heat. Add chicken into skillet and season with salt. Cook until chicken is browned, about 5 minutes.
Add in carrots and cabbage and cook until tender and the chicken is completely cooked through, about 5 to 7 minutes.
Pour sauce over veggies and let cook 2 to 3 minutes, stirring constantly.
Add in cooked noodles and toss to combine. Garnish with sliced green onion.
