Slice chicken into long strips roughly 1/8" thick. In a bowl, combine sesame seeds, peanut oil, and cornstarch. Add chicken and stir to coat.
Bring water to a boil in a large pot. Quickly blanch broccoli, boiling for 2 minutes. Drain and plunge into ice water or place broccoli under cold running water to halt the cooking process. Set aside.
In a wok or thin sauté pan, heat oil over medium heat. Sauté ginger and onion until the onion begins to soften and gently brown. Add garlic, cooking for about 30 seconds or until fragrant. Add chicken and cook through without browning.
Meanwhile, combine sesame oil, oyster sauce, soy sauce, water, and cornstarch in a measuring cup and stir vigorously. Pour sauce over chicken and add broccoli. Bring to a boil to thicken. Serve over steamed rice.