Place chicken drummers in a resealable plastic bag with the teriyaki sauce and let marinate 4 hours or overnight.
Preheat oven to 400˚F.
Place a cooling rack over a baking sheet and arrange chicken legs on it. Season chicken liberally with coarse black pepper.
Cover chicken legs with foil and roast 20 minutes. Turn legs and roast 10 minutes more. Remove foil and roast an additional 5-8 minutes to darken and crisp. Sprinkle with sesame seeds.
While the chicken cooks, bring stock and water with 1 tablespoon vegetable oil to a boil over high heat. Add rice and stir, bring back up to a boil then reduce heat and cover pot. Simmer 18 minutes then fluff with fork.