Pat the chicken thighs dry with paper towels. Season both sides with salt and black pepper. Smash the garlic cloves lightly with the flat of a knife and slice the ginger into 1/8-inch slices. Trim the white parts of the green onions and tie together with kitchen twine (or keep loose).

Brown the chicken

Heat a large heavy-bottomed skillet or Dutch oven over medium-high heat. Add the vegetable oil. When shimmering, place the chicken thighs skin-side down and brown until deep golden, about 4–5 minutes. Flip and brown the other side for 2 minutes. You are not cooking through—just rendering fat and building color. Transfer chicken to a plate and reserve any rendered fat in the pan.

Build the braising liquid

Reduce heat to medium. Add the smashed garlic, sliced ginger and white green onion pieces to the pan; sauté 30–45 seconds until fragrant, scraping up any browned bits. Pour in the Shaoxing wine and deglaze, scraping the bottom. Add the light soy sauce, dark soy sauce, brown sugar, star anise and 2 cups water. Stir to dissolve sugar and bring the liquid to a gentle simmer.

Braise the chicken

Return the browned chicken thighs to the pan, skin-side up. Nestle the bamboo shoots and carrot batons around the chicken so everything is partially submerged. Bring the liquid to a slow simmer, then cover the pan with a tight-fitting lid and reduce heat to low. Simmer gently for 25–30 minutes, turning the thighs once halfway through to coat them in sauce. Check for doneness: internal temperature should reach 74°C (165°F) and juices should run clear.

Reduce and finish sauce

Remove the lid and increase heat to medium. Carefully transfer the chicken pieces to a plate and tent with foil to keep warm. Boil the braising liquid until it reduces slightly and concentrates, about 4–6 minutes. Mix cornstarch with cold water to make a slurry and whisk into the simmering sauce to thicken slightly — about 1–2 minutes until glossy. Stir in 1 tsp sesame oil to finish. Taste and adjust seasoning with a pinch of salt if needed.

Return chicken to sauce

Return the chicken to the pan for 1–2 minutes to coat in the glossy sauce, spooning sauce over skin. Remove from heat.

Vegetable accompaniment & garnish

Blanch and season bok choy

Bring a medium pot of salted water to a boil. Add halved baby bok choy and blanch for 45–60 seconds until bright green and just tender. Remove and plunge into an ice bath to stop cooking, then drain well.

Warm carrots and bamboo shoots

While the chicken braises, heat a small skillet over medium heat with 1 tsp vegetable oil. Add the carrot batons and sauté 2–3 minutes until just tender-crisp. Add the drained bamboo shoots and sauté another 1–2 minutes until heated through. Season with 1 tsp light soy sauce and 1 tsp sesame oil, toss to coat.

Plate vegetables

Arrange the blanched bok choy and sautéed carrots/bamboo shoots on a serving platter or individual plates. Spoon a little of the reduced braising sauce over the vegetables for flavor.

Garnish

Slice the green parts of the green onions thinly and sprinkle them over the chicken and vegetables. Finish with toasted sesame seeds and optional chili oil or pickled chilies for heat.

Sauce finishing & serving

Serve

Serve the braised chicken hot over cooked jasmine rice. Spoon extra sauce from the pan over the rice and chicken so each serving has glossy, savory juices. Offer optional pickled chilies or chili oil at the table.

Leftovers and storage: Cool leftovers to room temperature, transfer to an airtight container and refrigerate up to 3 days. Reheat gently in a skillet with a splash of water, covered, until warmed through.