Place the chicken breasts into the crockpot.
In a bowl, whisk together soy sauce, hoisin sauce, oyster sauce, brown sugar, garlic, ginger, chicken broth, and sesame oil.
Pour the sauce mixture over the chicken and add the carrots and bell peppers.
Cover and cook on LOW for 4–5 hours or HIGH for 2–3 hours, until the chicken is tender.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
Cook the lo mein noodles according to package directions, then drain.
Add the cooked noodles and shredded cabbage (or broccoli) to the crockpot and toss to combine.
Mix cornstarch and water in a small bowl, then stir into the crockpot to thicken the sauce.
Cook for another 10–15 minutes until the sauce thickens.
Garnish with sliced green onions and serve warm.