In a medium bowl, whisk together the teriyaki sauce, soy sauce, brown sugar, rice vinegar, grated ginger, and minced garlic until the sugar is fully dissolved.

Place the chicken thighs or breasts in the bottom of a 6-quart slow cooker (Crockpot). Pour about three-quarters of the prepared teriyaki sauce mixture over the chicken, ensuring everything is coated.

Cover the slow cooker and cook on LOW for 6 to 8 hours, or on HIGH for 3 to 4 hours, until the chicken is easily shreddable.

Once cooked, remove the chicken from the slow cooker and shred it using two forks. Return the shredded chicken to the slow cooker liquid.

In a small bowl, whisk together the cornstarch and 2 tablespoons of cold water to create a slurry. Stir this slurry into the sauce remaining in the Crockpot. Cover and cook on HIGH for an additional 15-20 minutes, or until the sauce has thickened nicely.

Stir the shredded chicken back into the thickened teriyaki sauce until every piece is coated. Taste and add the remaining reserved sauce if a stronger flavor is desired.

Serve hot over steamed rice or noodles, garnished with toasted sesame seeds and fresh sliced green onions.