This recipe is for the chicken. Cook the rice and broccoli as desired. If you have one I definitely recommend using a rice cooker, as you can start the rice well ahead of time and the cooker will keep it warm and ready to go for when the chicken is done!
Cut the chicken into small bite-sized pieces and place into a small bowl. Liberally season with salt and pepper and toss to coat.
In a large nonstick skillet, heat up the vegetable oil over medium high heat. As soon as the oil begins to smoke, add the chicken pieces and allow to cook, tossing/turning to make sure all the sides are cooked. This should only take a few minutes; I recommend using a thermometer and checking the internal temp of the largest piece in your skillet--they'll be done when it reaches 165°F.
While the chicken cooks, in a small bowl add the brown sugar, soy sauce, garlic, vinegar, cornstarch, ginger, and optionally the red pepper flakes for a little spice. Whisk together until there are no cornstarch clumps left. Once the chicken is done, reduce the heat to medium and add the sauce. Stir constantly until the sauce thickens and coats the chicken; it will thicken quite dramatically so don't stop if the sauce is still watery.
Once done, serve in a bowl with rice and broccoli, and garnish with green onion and sesame seeds.
Enjoy!