Rinse chicken and pat dry. Set a 12-inch frying pan or a 5- to 6-quart pan over high heat. When hot, add oil and ginger; stir often until ginger is lightly browned, 3 to 4 minutes. Reduce heat to medium-high; push ginger to edges of pan and add chicken pieces, skin side down, in a single layer. Cook, turning once, until browned on both sides, 7 to 8 minutes total. Drain off and discard fat from pan.
Stir broth, 1/2 cup water, sugar, soy sauce, and salt into pan around chicken. Cover and bring to a boil, then reduce heat to medium and simmer 8 minutes. Turn chicken pieces over, cover, and continue cooking until no longer pink at the bone (cut to test), 7 to 9 minutes longer.
With tongs, lift chicken from pan juices and place in a shallow bowl or on a rimmed platter. Skim and discard fat from pan juices; pour juices over chicken. Sprinkle green onions on top of meat if desired.