Slice the chicken thighs into thin strips and the cabbage into thin ribbons. Keep them separate; they cook in turns.
Heat half the oil in your widest pan until it shimmers hard. Sear the chicken strips in a single layer, undisturbed for 2 minutes, then toss until just cooked through, about 2 more. Remove to a plate.
Add the remaining oil and the cabbage. Press it flat and leave it alone for 3 full minutes, until the underside chars in black-edged spots, then toss and char 3 minutes more.
Push the cabbage aside, drop the ginger and garlic into the pan's clear center for 30 seconds until fragrant.
Return the chicken with its juices, add the soy sauce, and toss everything together for 1 minute.
Kill the heat, scatter the green onions over, and serve straight from the pan.