1. In a deep 3- to 4-quart pan over high heat, uncovered, bring wine and 2 cups water to a boil. Add chicken and return to a boil. Remove from heat and cover tightly. Let stand until chicken is no longer pink in center of thickest part (cut to test), 15 to 18 minutes. Lift chicken from cooking liquid and let stand until chicken and liquid are cool, about 1 hour. Return chicken to cool liquid, cover, and chill for at least 2 hours or up to 1 day (see notes).
2. Lift chicken from liquid. Cut chicken crosswise into 1/4-inch-thick slices. Arrange slices, slightly overlapping, on a small platter. In a small bowl, mix soy sauce with 3 tablespoons of the cooking liquid; drizzle evenly over chicken. Reserve remaining cooking liquid to make broth, or discard.
3. Sprinkle green onions and cilantro over chicken. Pour oil into a 6- to 8-inch frying pan over high heat; when it ripples, in about 30 seconds, add ginger and chilies and stir until they sizzle, 10 to 15 seconds. Spoon mixture evenly over chicken.
You can complete step 1 up to 1 day ahead; the wine flavors the chicken more intensely when it stands overnight.