Prep everything first. Stir fries move fast. Slice the chicken thinly against the grain.
Shred the cabbage, slice the onion and carrot, and mince the garlic and ginger. Stir the sauce ingredients together in a small bowl; add the cornstarch slurry if you want a glossy, thicker finish.
Heat the pan properly. Use a large skillet or wok over medium-high heat. Add 1 tablespoon oil and let it shimmer before adding anything else.
Sear the chicken. Add the chicken in a single layer.
Sprinkle with a pinch of salt. Cook 3–4 minutes, stirring occasionally, until lightly browned and just cooked through. Transfer to a plate.
Aromatics time. Add the remaining 1 tablespoon oil.
Toss in the onion, garlic, ginger, and the white parts of the green onion. Stir fry 30–45 seconds until fragrant.
Add the veggies. Add the carrot and shredded cabbage. Stir fry 3–5 minutes until the cabbage softens slightly but still has crunch.
You want steam and sizzle—if the pan looks dry, add a splash of water to help it along.
Combine and sauce. Return the chicken to the pan. Pour in the sauce and toss to coat. If using a cornstarch slurry, you’ll see it thicken in about 30–60 seconds.
Add sesame oil and the green parts of the green onion. Taste and adjust with a bit more soy or vinegar as needed.
Serve hot. Spoon over rice or toss with noodles. Finish with sesame seeds and a squeeze of lime if you like.