Cut the chicken into 1 inch cubes and add to a bowl. Over the chicken add soy sauce, rice vinegar, cornstarch and ginger . Mix well and set to the side.
Wash and chop your broccoli in bite sized florets. Set aside.
Heat a large skillet or wok over medium-high heat and add the sesame oil and vegetable oil. When the oil is hot, add in the garlic and minced ginger. Add the chicken so the bottom of the pan is covered but not overcrowded. You may have to cook it in two batches.
When the chicken is browned on all sides and cooked through, remove it to a plate and repeat with the remaining chicken.
Measure out the sauce ingredients, mix them and set aside.
Add the broccoli florets to the hot skillet and stir fry for a few minutes. Make sure the broccoli stays vibrant in colour and maintains some crispy texture.
Add the chicken (with the juices on the plate) back in and mix together. Add the sauce ingredients to the pan and mix them well until you get a nice, velvety sauce that thickens slightly.
Serve over rice or noodles.