Prep the veggies and sauce: Thinly slice the cabbage and onion, shred the carrots, mince the garlic, and grate the ginger. In a small bowl, whisk soy sauce, rice vinegar, sesame oil, chili-garlic sauce, and brown sugar or honey. If using cornstarch, dissolve it in 1 tablespoon of water and stir into the sauce.
Heat the pan: Set a large skillet or wok over medium-high heat.
Add 1 tablespoon of neutral oil and swirl to coat.
Brown the chicken: Add ground chicken, season with a pinch of black pepper, and break it up with a spatula. Cook until no longer pink and lightly browned, about 4–6 minutes. If the pan seems dry, add another small splash of oil.
Flavor base: Push chicken to one side.
Add a little oil if needed, then sauté the onion for 1–2 minutes. Add garlic, ginger, and the white parts of the green onions. Cook until fragrant, about 30–60 seconds.
Stir everything together.
Add veggies: Add the cabbage and carrots. Toss well and cook, stirring often, until the cabbage softens but still has some bite, 4–6 minutes. If the pan looks crowded, cook in batches or cover for 1–2 minutes to help it steam, then uncover to finish.
Sauce it up: Give the sauce a quick stir and pour it over the chicken and vegetables.
Toss to coat and cook for 1–2 minutes, until the sauce slightly thickens and clings to the cabbage.
Taste and adjust: Add more soy for salt, chili-garlic for heat, or a splash of rice vinegar for brightness. If it needs more moisture, add 1–2 tablespoons of water.
Finish and serve: Sprinkle in the green onion tops and sesame seeds. Serve hot as-is, over rice, or with noodles.