How to Make It
In a large, deep skillet, heat the oil until shimmering. Season the chicken lightly with salt and pepper and add to the skillet skin side down. Cook over moderately high heat, turning occasionally, until browned all over, 10 to 12 minutes. Transfer the chicken to a plate.
Add the onion to the skillet and cook over moderate heat, stirring occasionally, until softened and browned, about 7 minutes. Add the ginger, star anise, chiles and garlic and cook, stirring, until fragrant, about 1 minute. Add the wine, soy sauce, sugar and chicken stock and bring to a boil. Add the potatoes and carrots and return to a boil. Nestle the chicken in the skillet, cover and braise over moderately low heat, turning occasionally, until the vegetables are tender and the chicken is cooked through, 15 to 20 minutes. Discard the star anise and chiles.
Meanwhile, in a medium saucepan, cover the eggs with water and bring to a boil. Simmer over moderate heat for 8 minutes, then cool under running water. Peel the eggs and quarter lengthwise.
Gently submerge the eggs in the stew and spoon into shallow bowls. Garnish with chopped cilantro and scallions and serve with steamed rice.