Warm the vegetable oil in a large pot over medium heat.
Add the ground pork or turkey and cook, breaking it apart until it's fully browned, about 5 to 7 minutes.
Mix in the diced onion, garlic, and grated ginger, cooking until the onion softens and becomes fragrant, around 2 to 3 minutes.
Pour in the broth and bring the soup base to a gentle simmer.
Add the coleslaw mix, stirring occasionally until the vegetables soften, about 5 minutes.
Combine soy sauce, sesame oil, rice vinegar, and black pepper in a small bowl, then stir this mixture into the pot.
Let the soup simmer gently for 5 to 10 more minutes to deepen the flavors.
If using noodles, fold them in right before serving to warm through.
Dish out the soup in bowls and sprinkle with sliced green onions as a finishing touch.