Mix together garlic, ginger, 1 cup water, soy sauce, and brown sugar. Reserve 1 cup for the teriyaki sauce. Pour remaining mixture over chicken, stir to coat evenly, cover, and marinate in the fridge for at least 30 mins, up to overnight.
Preheat a large skillet over medium high heat and add avocado oil. Let excess marinade drip off the chicken, then sear for 5-6 mins per side, until charred and internal temp reaches 165F. Transfer to a plate and let rest.
In a small pot over medium heat, warm the reserved teriyaki sauce for 1-2 mins. Whisk cornstarch with 1 tbsp water, then pour into the sauce and whisk. Cook until bubbling and thickened, 1 to 2 mins, then remove from heat and stir in white vinegar.
Add the chicken, along with any resting juices, to the sauce and toss to coat.
Sprinkle broccoli lightly with salt and place in a microwave safe bowl with 2 tbsp water. Cover and microwave 2-4 mins until bright green and tender.
Slice the chicken and serve over warm rice with broccoli and extra teriyaki sauce drizzled on top.
