Prepare the vegetables and keep the raw chicken on a separate plate. Add the olive oil and onion to a heavy 6-quart pot over medium-low heat. Stir for 2–3 minutes without browning. Add the napa cabbage, carrots, mushrooms, garlic, half the ginger, and half the salt.

Cover closely and reduce the heat to low. Cook for 12–15 minutes, until the cabbage has collapsed and there is visible liquid at the bottom. Check briefly and stir gently once. If the vegetables remain dry, continue covered on very low heat for another 5 minutes and check again. Do not add the chicken to a pot that is scorching; remove from heat and reassess the pot and heat instead.

Nestle the chicken thighs among the softened vegetables. Add the remaining ginger, salt, and pepper. Cover tightly and cook at a very gentle simmer over low heat for about 30–40 minutes. Avoid frequent lid lifting, and lower the heat if it boils hard. No water or stock is added.

Check several thick thighs with a thermometer; chicken must reach at least 165°F (74°C). Continue gently if needed until the chicken is safe and tender. Remove the thighs with clean tongs, divide into bite-size pieces on a clean board, and return them to the pot.

Stir gently and divide chicken, vegetables, and all the natural juices among four bowls. Expect a concentrated shallow broth, with the amount varying by cabbage and lid fit. Refrigerate leftovers in shallow containers within 2 hours, use within 3–4 days, and reheat to 165°F (74°C).