Step #2 In a large, onion, wide saucepan, garlic, hoisin sauce, rice vinegar, mix together sesame oil, soy sauce, broth, apricot preserves, light brown sugar & ginger; mix well.
Step #3 Heat mixture to a boil over med-high heat.
Step #4 Add the chicken drumsticks.
Step #5 Continue to cook over medium to medium-high heat for 25-30 mins, turning/rearranging chicken (with tongs) often, or until chicken juices run clear.
Step #6 Remove chicken to a platter; keep warm.
Step #7 IF the sauce has not yet reduced to a thick glaze yet, continue to cook & stir until it reduces to a thick glaze; do not let burn.
Step #8 Either Pour the reduced glaze over chicken pieces or return the chicken to the galze in the pot (off the heat) & stir this to coat.
Step #9 Sprinkle top with sesame seeds and/or sliced green onions, if desired.