Place the chicken breasts pieces into the 2-quart slow cooker.
Whisk together the garlic, ginger, honey, brown sugar, soy sauce, sesame oil and rice vinegar, then pour the mixture over the chicken.
Cover and cook on HIGH for 3 hours and 45 minutes.
Add the red pepper, hot pepper, carrots, gently stir to combine, cover, and cook for 20 minutes.
Add the broccoli and mushrooms, stir, cover, and cook for 20 minutes more.
Using a slotted spoon, remove the chicken and vegetables from the slow cooker to a rimmed sheet pan or platter, cover and set aside. (Optional - at this point I separate the chicken from the vegetables to serve the chicken on rice and the vegetables on the side)
Strain the remaining teriyaki sauce from the slow cooker into a small saucepan.
Place the saucepan on the stove over medium-high heat and bring to a low boil.
In a small bowl, mix a slurry of the cornstarch and water until fully dissolved. Then pour the cornstarch into the saucepan, stir, bring back to a low a boil. Cook for 3-4 minutes, stirring occasionally, until sauce has just thickened.
Pour half the sauce over the chicken pieces and toss to coat.
Garnish with a sprinkle of sesame seeds, green onions, red onions, then serve. Enjoy!