Place the chicken breasts or thighs in the bottom of the slow cooker.
In a bowl, whisk together soy sauce, honey or brown sugar, rice vinegar, sesame oil, garlic, and ginger.
Pour the sauce mixture over the chicken, ensuring it is well coated.
Cover and cook on low for 4–5 hours or on high for 2–3 hours, until the chicken is tender and fully cooked.
Remove the chicken from the slow cooker and shred it using two forks.
In a small bowl, mix cornstarch and water to create a slurry.
Stir the slurry into the sauce in the slow cooker and turn the heat to high. Cook uncovered for 10–15 minutes until the sauce thickens.
Return the shredded chicken to the slow cooker and stir to coat evenly with the thickened sauce.
Prepare rice and vegetables while the sauce thickens.
Assemble bowls by layering rice, teriyaki chicken, and vegetables. Garnish with sesame seeds and green onions.