Mix the first six ingredients in a sealable plastic bag to blend. Add the chicken drumsticks, seal the bag and toss to coat. Refrigerate for at least one hour or overnight.
Position your oven rack 8 to 10 inches from the heat sources of your broiler and preheat the broiler. line a large, rimmed baking sheet with heavy-duty foil. Arrange the drumsticks and the marinade on the sheet and broil, turning often and watching carefully. The sugar in the marinade causes the drumsticks to char so by turning often you get nicely, lightly, charred drumsticks. Also, turning them often glazes them nicely with the marinade in the pan. Broil them for 25 minutes.
Sprinkle the sesame seeds over the chicken and serve.