Place the chicken breasts in the bottom of a slow cooker.
In a small bowl, stir together the garlic, ginger, honey, brown sugar, soy sauce, rice vinegar, and sesame oil. Pour over the chicken.
Cook on high for 3-4 hours or low 6-7 hours.
Remove chicken from the slow cooker and shred with two forks.
Pour the sauce in the slow cooker through a strainer into a sauce pan. Bring mixture to a simmer over medium heat.
In a small bowl, mix the cornstarch with the water. Pour mixture into the sauce pan. Stir and bring to a boil for a few minutes to thicken.
Pour sauce over chicken and toss to coat. I like to keep the mixture in the crockpot on warm. Sprinkle with sesame seeds and green onions when serving.