Arrange the chicken breasts in the slow cooker in an even layer. The chicken should sit flat so the sauce can surround it evenly as it cooks.
Whisk the garlic, ginger, honey, brown sugar, low sodium soy sauce, toasted sesame oil, and rice vinegar in a small bowl until blended. You’ll smell the ginger and garlic right away, and the sugar should look dissolved into the dark sauce.
Pour the sauce mixture over the chicken. Make sure the tops of the chicken pieces are coated so they start absorbing flavor immediately.
Cover and cook on HIGH for 3 hours or LOW for 5-6 hours. The chicken is ready when it looks opaque throughout and shreds with very little resistance.
Transfer the cooked chicken to a plate or bowl, then pull it apart with two forks. If the chicken fights back while shredding, it likely needs a little more cooking time.
Strain the cooking liquid from the slow cooker into a saucepan. Straining removes bits of garlic and ginger for a smoother, silkier finished sauce.
Set the saucepan over medium high heat and bring the sauce to a simmer. As it heats, the aroma becomes sweeter and more concentrated.
Stir the cold water and cornstarch together in a small bowl until completely smooth. The slurry should look milky with no dry cornstarch settled at the bottom.
Whisk the cornstarch mixture into the simmering sauce, bring it to a boil, and cook for 1-2 minutes. The sauce is ready when it turns glossy and coats the back of a spoon.
Toss the shredded chicken with the thickened sauce, then finish with sesame seeds and sliced green onions. Let the chicken get evenly coated so every strand looks shiny and well glazed.