Cook and drain the noodles according to the package instructions.
In a bowl, season shrimp with salt and pepper.
Heat a large skillet with 1 ½ tablespoons of the oil over medium-high heat. Cook the shrimp until it turns pink and opaque, about 3 minutes. Transfer the shrimp from the skillet to a bowl or plate.
In the same skillet, heat the rest of oil and the add the cabbage, carrot, and bell pepper and cook, stirring occasionally, until the vegetables soften, about 4 minutes. Add the ginger and garlic and cook, stirring, for another minute or so.
Meanwhile, make the sauce by stirring together the soy sauce, oyster sauce, hoisin sauce, vinegar, and sesame oil in a bowl.
Add the noodles to the skillet with the vegetables, the reserved shrimp, and the sauce mixture and toss until well combined and heated through.
Serve hot, garnished with green onions.