Transfer chicken to a serving bowl and keep warm, covered.
Skim off any fat from sauce and boil sauce until syrupy and reduced by half, 15 to 20 minutes. Stir cornstarch mixture and whisk into sauce. Boil, whisking, until thickened and shiny, about 1 minute. Discard ginger and star anise.
Pour sauce over chicken and sprinkle with scallions.
Cooks' note: Use a paper towel to blot up any last bits of fat from surface of sauce after skimming.