Heat sesame oil and neutral oil in a large skillet over medium-high heat.
Add ground chicken, salt, and pepper. Cook, breaking it apart with a spatula, until browned and slightly crispy, about 7–9 minutes.
Stir in the onion, garlic, and ginger. Sauté until the onion is soft and fragrant, about 2–3 minutes.
Mix in the coleslaw mix (or shredded cabbage and carrots) and cook for 2–3 minutes, just until the vegetables are slightly wilted but still crisp.
Pour in soy sauce, oyster sauce, and rice vinegar. Stir to evenly coat the mixture and combine flavors.
Taste the mixture and adjust seasoning. Add more soy sauce or sriracha/chili garlic sauce for extra kick, if desired.
Stir in chopped green onions. Serve hot, garnished with toasted sesame seeds, crispy onions, or additional green onions.