Heat a large skillet over medium heat. Once hot, add oil and broccoli. Cook, shaking the pan often, until broccoli begins to sear and get some brown spots. After 5 minutes, add 2 tablespoons of water to slightly steam the broccoli. Cook until bright green, slightly tender but still crisp.
Meanwhile, whisk together the soy sauce and cornstarch in a bowl. Add remaining ingredients to the bowl and whisk. Pour over the broccoli in the skillet and cook for 2 minutes, stirring often, until the sauce is thickened and the broccoli is coated. Sprinkle with sesame seeds if desired.