Cook the lo mein noodles in a pot of boiling water according to package directions. Drain.
Whisk together the broth, soy sauce, hoisin sauce, oyster sauce, sesame oil and cornstarch until smooth and set aside.
At the same time as you are working on step one (boiling water for noodles), drizzle the oil in a large saute pan and bring over med-high heat. Add the chicken to the hot oil and sprinkle with salt and pepper. Stir to coat. Cook for 5-8 minutes, stirring occasionally, until chicken is cooked through. Remove the chicken to a side plate.
Add the onions to the hot pan and reduce the heat to med-low. Cook the onions for 4-5 minutes, stirring occasionally, until softened and a bit golden. Add the garlic and ginger and stir. Cook for an additional 30-60 seconds until fragrant. Add the cabbage, snow peas, and carrots and stir together. Cook for another 2-3 minutes, stirring occasionally. Add the chicken and cooked, drained noodles to the pan and stir to combine.
Add the sauce you whisked together in step 2 to the pan and stir to coat the noodles and ingredients. Cook for another minute and sprinkle with the scallions before serving.