Cook the lo mein noodles according to package instructions until al dente. Drain, rinse under cold water, and set aside.
In a small bowl, whisk together soy sauce, oyster sauce, hoisin sauce, sesame oil, cornstarch, and chicken broth until smooth. 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, season with salt and black pepper, and cook until the chicken is no longer pink and lightly browned, about 5-6 minutes. Remove the chicken from the skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet. Add the garlic and ginger and sauté for 30 seconds until fragrant.
Add the carrot, snap peas, and cabbage to the skillet. Stir-fry the vegetables for 3-4 minutes until they are tender-crisp.
Return the cooked chicken to the skillet with the vegetables. Pour the sauce mixture over the chicken and vegetables and stir well to coat. Cook for 2 minutes until the sauce thickens slightly.
Add the cooked noodles and sliced green onions to the skillet. Toss everything together gently to combine and heat through for 1-2 minutes.
Remove from heat and let the lo mein cool completely before packing for freezing.
To freeze: Portion the cooled chicken lo mein into airtight freezer-safe containers or heavy-duty freezer bags. Label with the date and freeze for up to 3 months.
To reheat: Thaw overnight in the refrigerator. Reheat in a skillet over medium heat until warmed through, adding a splash of water or chicken broth if needed to loosen the sauce.