Cook white and pale green parts of scallions, chiles, and ginger in same pot, stirring often, until scallions and ginger are golden, about 3 minutes. Add wine, bring to a simmer, and cook until reduced to about 3 Tbsp., 5 minutes. Add soy sauce, brown sugar, sesame oil, and 1 cup broth and bring to a simmer, stirring to dissolve sugar. Return chicken to pot, placing skin side up and overlapping if needed. Partially cover pot, reduce heat, and simmer until chicken is cooked through, 25–30 minutes. Transfer chicken to a plate.